{
  "title": "Geometric Structure Spaces",
  "record_type": "LFH_PROJECT_MANIFEST",
  "derived_view": true,
  "identity": {
    "slug": "geometric-structure-spaces",
    "title": "Geometric Structure Spaces"
  },
  "status": {
    "publication_edition": "Version 1",
    "selected_cards": 69,
    "catalog_selection": "EXACT_REVISION_SET",
    "publication_date": "2026-11-02"
  },
  "cards": [
    {
      "node_id": "1",
      "declaration": "ClosureSpace",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:051c8b2fd731474cb5638761a359e66ab04e78beb04386598bdb1e8e977cc048",
        "revision": 1,
        "sha256": "1920461172d18ea8206dbdbd7a0ece11093e458889a720c183e5baefb6c25d97"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "b29f460ba05d2dd1333a2a3fb82e431b8733bf32fca1a27f618cfeeb6c7a89de"
      },
      "manuscript_sha256": "4cac2496ebf2f2ea927aae150a194274bdec49dcca513ba261e3a4df9dedf4cf",
      "guide_sha256": "4aca0024df6db0dcc992761bcbc9258a6fd55a368e336593ce41b0ba4de76abc",
      "url": "../../cards/051c8b2fd731474cb5638761a359e66ab04e78beb04386598bdb1e8e977cc048/versions/gss-r1-b29f460ba05d2dd1/index.html",
      "card_json": "../../cards/051c8b2fd731474cb5638761a359e66ab04e78beb04386598bdb1e8e977cc048/versions/gss-r1-b29f460ba05d2dd1/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Basic.lean.html?from=1&start=28&end=30#L28",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/Basic.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Basic.lean",
        "raw_bytes": {
          "bytes": 4509,
          "sha256": "985a7e7c4fb1e2a2a299c7cf8874531bbfacd31d2ef0cdace6efeb4dd0607c3a"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "38",
      "declaration": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:36ad36607b1a349c8b0647a7d6e199c5c46b6c514e202fbb2a51742ba95929c3",
        "revision": 1,
        "sha256": "8bb6620137801883e60f145cf1d70dcac0458b64e972d628da64877bb86b9b67"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "cf4dbb68d9349dd9c30204df7b0f5d5e0000f7393367c42de604ca3cf56fbd35"
      },
      "manuscript_sha256": "76ed31b6c4108aeb954f510c05c0330af9c61753d63e879b8cf794bf24a1cd38",
      "guide_sha256": "4ff5ebb1d51ceba3af88fbb39d26a3c6798931b3d0773d1bd9ad0b2f3cf12c9d",
      "url": "../../cards/36ad36607b1a349c8b0647a7d6e199c5c46b6c514e202fbb2a51742ba95929c3/versions/gss-r1-cf4dbb68d9349dd9/index.html",
      "card_json": "../../cards/36ad36607b1a349c8b0647a7d6e199c5c46b6c514e202fbb2a51742ba95929c3/versions/gss-r1-cf4dbb68d9349dd9/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/Module/SemilinearRegularity.lean.html?from=38&start=291&end=302#L291",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/Module/SemilinearRegularity.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/Module/SemilinearRegularity.lean",
        "raw_bytes": {
          "bytes": 15216,
          "sha256": "51dde79b6ffcfc7a63139d8716e3b044072d6a4f905796afb377c65aacfdf2f2"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "c0-direct-sum",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:613580e7a78da1e407fd973eb4a29fa79a46f0cd91a0f390c35e2d30e0c1ace1",
        "revision": 1,
        "sha256": "baac453b94b53f8dd3b5522e5a8dafb6524316acbcc0e4fbf0e8484d681370e9"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "caf05679cdf0546bdc7c088c3dabfd7cdf145fe08ec184814204cab72f63b596"
      },
      "manuscript_sha256": "e55fba268c8c8ab6515a7e96ee1ce1c36174a0b6a96b2f4fc4c55c2faa57b467",
      "guide_sha256": "8d8b51bfd563d90848ec3190506685b9d1920096c79e19db284698a1531cfa5c",
      "url": "../../cards/613580e7a78da1e407fd973eb4a29fa79a46f0cd91a0f390c35e2d30e0c1ace1/versions/gss-r1-caf05679cdf0546b/index.html",
      "card_json": "../../cards/613580e7a78da1e407fd973eb4a29fa79a46f0cd91a0f390c35e2d30e0c1ace1/versions/gss-r1-caf05679cdf0546b/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/C0DirectSum.lean.html?from=c0-direct-sum&start=225&end=227#L225",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/C0DirectSum.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/C0DirectSum.lean",
        "raw_bytes": {
          "bytes": 13647,
          "sha256": "c62f1b8c28a6d41292e0210269d200ebc2913f195946e796ee93fbf884113693"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "irreducible-spectrum",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:6d61411eb406741fdc311de8512a3c787026dbe4ac5fdd13f4ee8e3f9f8e5f36",
        "revision": 1,
        "sha256": "4861864cbf4bde81b34c1eb6b8db30c4cf86345f85100e102aa041dc8fed8863"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "50deff8011e46124c6044e84afac7a08f72867338db375c1908f371454ce7876"
      },
      "manuscript_sha256": "7d44a46e3623ee44f4c8b56160ce0b49d6fbaea02e10b66b1b1ede5eb94af729",
      "guide_sha256": "366d4a9eee24e6be511030b881ef6fac407d4f33d12086ed85641084fba8c77d",
      "url": "../../cards/6d61411eb406741fdc311de8512a3c787026dbe4ac5fdd13f4ee8e3f9f8e5f36/versions/gss-r1-50deff8011e46124/index.html",
      "card_json": "../../cards/6d61411eb406741fdc311de8512a3c787026dbe4ac5fdd13f4ee8e3f9f8e5f36/versions/gss-r1-50deff8011e46124/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/Basic.lean.html?from=irreducible-spectrum&start=73&end=73#L73",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/Basic.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/Basic.lean",
        "raw_bytes": {
          "bytes": 3996,
          "sha256": "ea93fd5c948babb9f9976d9367ff68e77e2ef3461539746fff4aff3401fe032a"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "is-compact-operator-model",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
        "revision": 3,
        "sha256": "4329259b4399443c46e9a493ef3081bde406d18a69b68d371617f4b64ca88f8d"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "5499220b48a8fdad92e384f2bc1a614467925550db22ed5b235596a3926a555f"
      },
      "manuscript_sha256": "2ccd05514cd6571908decd8a6e1d8a3991d3eeb9e9dcaf01b7070510bdeaeea8",
      "guide_sha256": "d640d0b8566257ea8525354777d4a81352e71a27795c169ca2acfe7a7c614066",
      "url": "../../cards/26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384/versions/gss-r3-5499220b48a8fdad/index.html",
      "card_json": "../../cards/26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384/versions/gss-r3-5499220b48a8fdad/card.json",
      "source_binding": {
        "source_view": "../../sources/lfh-v0.4.0/MathlibAnnex/Analysis/CStarAlgebra/CompactModel.lean.html?from=is-compact-operator-model&start=26&end=33#L26",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/437e6e46228bbb8e91211ebded349d7a30020e73/MathlibAnnex/Analysis/CStarAlgebra/CompactModel.lean",
        "raw": "../../raw/lfh-v0.4.0/MathlibAnnex/Analysis/CStarAlgebra/CompactModel.lean",
        "raw_bytes": {
          "bytes": 3652,
          "sha256": "d76879b349527cfdc65525d780a4f27f220bd19c8ab69e01f7b5bb87a1f8c285"
        },
        "release_scope": "v0.4.0"
      }
    },
    {
      "node_id": "primitive-spectrum",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:8f04eaabc6451d43c2e877d60ea2504bb4b937f2a0129f3789ea91fd53d5d568",
        "revision": 1,
        "sha256": "5a62cba0595026cc4bcc1122f62ebd940857f84d1c9d2b333632d3465c5b13bf"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "026b5249968b4adf1f789eaeca9c079efd31e765a4217128a219df13bcfb5cef"
      },
      "manuscript_sha256": "9b706a9e7388cff76770f33ec641c6dd64a23a96e8b715a082463b90e86956fd",
      "guide_sha256": "99eb64833134262df40274bc7758a00c33f61703355e4833393eacaec256e25a",
      "url": "../../cards/8f04eaabc6451d43c2e877d60ea2504bb4b937f2a0129f3789ea91fd53d5d568/versions/gss-r1-026b5249968b4adf/index.html",
      "card_json": "../../cards/8f04eaabc6451d43c2e877d60ea2504bb4b937f2a0129f3789ea91fd53d5d568/versions/gss-r1-026b5249968b4adf/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/Primitive.lean.html?from=primitive-spectrum&start=33&end=33#L33",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/Primitive.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/Primitive.lean",
        "raw_bytes": {
          "bytes": 6081,
          "sha256": "a283f23f3d1f991e4cf38564a7ce3c65820a99bbc60662b6b6f8b26745118df5"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "15",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:6687745b481cc7b6e73c7c61ba652b611a41578831abbe59a67455d6f87adb1a",
        "revision": 1,
        "sha256": "183dd516c87ce07c1d14c7fc61b30313085b853d29a27e5d46b2d8ed3bc59e71"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "127aee93a1a000f27a2688ffe32424e5ef4b38909715ae00ef58071f29cdc63e"
      },
      "manuscript_sha256": "174a4febdb29c7ee2aa156d240c5802ec777eb591ad5b435462e0a9ef0aeb1ec",
      "guide_sha256": "40484f661feab40b757423a0595d776231652a14fdcb3d48a52d48ed77172374",
      "url": "../../cards/6687745b481cc7b6e73c7c61ba652b611a41578831abbe59a67455d6f87adb1a/versions/gss-r1-127aee93a1a000f2/index.html",
      "card_json": "../../cards/6687745b481cc7b6e73c7c61ba652b611a41578831abbe59a67455d6f87adb1a/versions/gss-r1-127aee93a1a000f2/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/FacialStructure/ExtremeDecomposition.lean.html?from=15&start=61&end=81#L61",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/FacialStructure/ExtremeDecomposition.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/FacialStructure/ExtremeDecomposition.lean",
        "raw_bytes": {
          "bytes": 6480,
          "sha256": "77d9584147f3fcc8b44fa83e5daa8c21b7f2042e8c1c7ddbacabcf783f9e6c0f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "3",
      "declaration": "NormedSpace.supportKernelUnion",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:0d49049cbfbdb774584e35ddc6cb49a1befcb0813eff99dc399e90c62475da1a",
        "revision": 1,
        "sha256": "64324b7824e7944628e721b7af9729e584e7d2c1c5663efe355c931918a5fec3"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "5ba0666104ffcad2c24e7d6412133db4ae61eba40a4fec9fb7a09e0b3f72d7c2"
      },
      "manuscript_sha256": "b59ffeb803514c424d232797483ab72373304f0cb55544840a6bc832bf34aeac",
      "guide_sha256": "a55e948043ba2382544b8bff78d5596ac6fefb9930dc20249647d6000a820936",
      "url": "../../cards/0d49049cbfbdb774584e35ddc6cb49a1befcb0813eff99dc399e90c62475da1a/versions/gss-r1-5ba0666104ffcad2/index.html",
      "card_json": "../../cards/0d49049cbfbdb774584e35ddc6cb49a1befcb0813eff99dc399e90c62475da1a/versions/gss-r1-5ba0666104ffcad2/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Support.lean.html?from=3&start=42&end=45#L42",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Support.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Support.lean",
        "raw_bytes": {
          "bytes": 6822,
          "sha256": "4fbb8f62dcd2a9a1d4d2af20d6770a8098c643b162459c5d6c3b7cb6bfd96ca0"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "35",
      "declaration": "Projectivization.exists_semilinearEquiv_of_finite_span",
      "level": 0,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:58fdb50ad0831bf924e6577a8d8a2957d8e27df94e24525f3860b86d681d1c27",
        "revision": 1,
        "sha256": "9e4b04cf36edb925862f694349f56eef15b7249ca2e3b2841361ce9453d09af5"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "14dcd6e20d1ec8cc4d59dc4c4a542bd99d82e59c9bf3d87fee297cd610cc10cd"
      },
      "manuscript_sha256": "2eddab83cfeea74d55bbda2525c3f47d3e0fa972c62cabbc13123752f24414a5",
      "guide_sha256": "df90c6811b7dfe934ed4fa67448cd7376c2b812813c1357cb377a8a6e864f472",
      "url": "../../cards/58fdb50ad0831bf924e6577a8d8a2957d8e27df94e24525f3860b86d681d1c27/versions/gss-r1-14dcd6e20d1ec8cc/index.html",
      "card_json": "../../cards/58fdb50ad0831bf924e6577a8d8a2957d8e27df94e24525f3860b86d681d1c27/versions/gss-r1-14dcd6e20d1ec8cc/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/LinearAlgebra/Projectivization/Semilinear.lean.html?from=35&start=514&end=533#L514",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/LinearAlgebra/Projectivization/Semilinear.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/LinearAlgebra/Projectivization/Semilinear.lean",
        "raw_bytes": {
          "bytes": 27588,
          "sha256": "93f555c4b459b46388dcf866345d3d379b96cefb72f4aa7714eab5cc3a7f2f9f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "12",
      "declaration": "ClosureSpace.FiniteHomeomorph",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:a94dce0ec7355781265c5013b5a05fc406db350a4a465c398f735051defb2c03",
        "revision": 1,
        "sha256": "38a8f0214ce0fb421589596a6d983552506282203cf245988cce3624bcc1cf37"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "84659fc4c28b0535b7c50ace203805f74b471fe92077bb1732f046127ecb6349"
      },
      "manuscript_sha256": "503a5291e198ff42970e35ff56fd40f027f49c7e8fefef1ce01e797e195b5a55",
      "guide_sha256": "ea528e0e35b522e46cdfd2acaed69b425e6101a31898bee7a1e86eb8944226fe",
      "url": "../../cards/a94dce0ec7355781265c5013b5a05fc406db350a4a465c398f735051defb2c03/versions/gss-r1-84659fc4c28b0535/index.html",
      "card_json": "../../cards/a94dce0ec7355781265c5013b5a05fc406db350a4a465c398f735051defb2c03/versions/gss-r1-84659fc4c28b0535/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Maps.lean.html?from=12&start=157&end=159#L157",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/Maps.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Maps.lean",
        "raw_bytes": {
          "bytes": 7047,
          "sha256": "5a35a3a6f70dc294fd56e8cfa873c14cb3ba9e9f29f599486556162eec641ade"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "2",
      "declaration": "ClosureSpace.HullKernel.space",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:1f4222f50792ca031f258638df676d23702dccbafd0e99dfd4e3f2f5e7ba8721",
        "revision": 1,
        "sha256": "f4cc32639662f8f5db1218cfa73a2a29b0e04de4b1d6db03c3d8cb737e0b6e32"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "a6864444b7f937a88a77daec2a34c6c871d89c7410cedab37a6cbda6d00b9139"
      },
      "manuscript_sha256": "6f67a0d21cd17ab5badfd7f939508f613915235fb9b3c7d77d6eb230b70c1e80",
      "guide_sha256": "e2ab2cf261cec751b1c445b178153dc5731deb052ee7e1694329794a9821d46e",
      "url": "../../cards/1f4222f50792ca031f258638df676d23702dccbafd0e99dfd4e3f2f5e7ba8721/versions/gss-r1-a6864444b7f937a8/index.html",
      "card_json": "../../cards/1f4222f50792ca031f258638df676d23702dccbafd0e99dfd4e3f2f5e7ba8721/versions/gss-r1-a6864444b7f937a8/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/HullKernel.lean.html?from=2&start=30&end=31#L30",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/HullKernel.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/HullKernel.lean",
        "raw_bytes": {
          "bytes": 4313,
          "sha256": "084719fb3f3d66b942525701d1b129c3fe11a7543a777898af50a17d3a4cb46b"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "7",
      "declaration": "ClosureSpace.Linked",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:ed8be8d278e688abbaaaaf2aeb148c8fd09bf3b9526a455940aad9c2d0bcedeb",
        "revision": 1,
        "sha256": "5231bb6cea3d1a33294e8038a886849e69645314a865cf17a3d3473814803dfb"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "1076e655b13cc43caf1829500a9e8c7d1b671462cf8fd973ab988e71d22f98f6"
      },
      "manuscript_sha256": "29d18c963b72cee77e48beb18b53b4b9e94013521bf980363adc862ba536aba9",
      "guide_sha256": "c197c330256a71d3ba639ca3bae730d3c2e3eb8540a8ca094557a0c1b98b6127",
      "url": "../../cards/ed8be8d278e688abbaaaaf2aeb148c8fd09bf3b9526a455940aad9c2d0bcedeb/versions/gss-r1-1076e655b13cc43c/index.html",
      "card_json": "../../cards/ed8be8d278e688abbaaaaf2aeb148c8fd09bf3b9526a455940aad9c2d0bcedeb/versions/gss-r1-1076e655b13cc43c/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Components.lean.html?from=7&start=30&end=30#L30",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/Components.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Components.lean",
        "raw_bytes": {
          "bytes": 5940,
          "sha256": "f8a603680a6aa871b86d4c994dcec4514d7470deadf9a60466e110a9f572fd4f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "ideal-c0-sum-equivalence",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:8a8d58440958063c8cb597bb8de63288b0af0efc3cff567f92a54e5a55288c77",
        "revision": 1,
        "sha256": "ff3deda7d520dc409ec71398699434e14b65bfa179c7712a82ce4ea242fb3cb8"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "975d408df450cf796fea3d8d5ff0a864e16544e679d153cbfcd315dd9ad06501"
      },
      "manuscript_sha256": "49aec58501a27b8da155f6c53435ba379848b959b29b08da1783b96d92802c64",
      "guide_sha256": "a1ac19fdbd4aaa3e658f2ee45e044439b8a8d2b39b20ca3639c0a92cbe6d79d5",
      "url": "../../cards/8a8d58440958063c8cb597bb8de63288b0af0efc3cff567f92a54e5a55288c77/versions/gss-r1-975d408df450cf79/index.html",
      "card_json": "../../cards/8a8d58440958063c8cb597bb8de63288b0af0efc3cff567f92a54e5a55288c77/versions/gss-r1-975d408df450cf79/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/OrthogonalIdealAssembly.lean.html?from=ideal-c0-sum-equivalence&start=589&end=599#L589",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/OrthogonalIdealAssembly.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/OrthogonalIdealAssembly.lean",
        "raw_bytes": {
          "bytes": 26501,
          "sha256": "68f9414a94aa4fc64b7979ba17a7faa1180f0004500474a21d6e7a1118391791"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "compact-operator-c0-sum",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:5cf0bcfe187a49cb7ede9d665be53ec0dfc990d1f18c10024ceb9120076696ed",
        "revision": 1,
        "sha256": "2f73021866e72dd25d244139fed61f1ee76e03fca90c88fd531984f1cc1e4bc3"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "c9c26d8f13af10e255ea0b7022188f076908e9e96f60c249c6c1f93ccf62ddb7"
      },
      "manuscript_sha256": "ea4f71e47292bee94ae7d3f86f83673d6901f26376a6738fa63079a026a20758",
      "guide_sha256": "5ae70ffb5f47b605d5669b0475a65da501105b01e34d4ab85fb6d9ac95c5bb30",
      "url": "../../cards/5cf0bcfe187a49cb7ede9d665be53ec0dfc990d1f18c10024ceb9120076696ed/versions/gss-r1-c9c26d8f13af10e2/index.html",
      "card_json": "../../cards/5cf0bcfe187a49cb7ede9d665be53ec0dfc990d1f18c10024ceb9120076696ed/versions/gss-r1-c9c26d8f13af10e2/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/CompactOperators.lean.html?from=compact-operator-c0-sum&start=28&end=32#L28",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/CompactOperators.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/CompactOperators.lean",
        "raw_bytes": {
          "bytes": 1111,
          "sha256": "6a59d66e9df29269621d2b968bee9a1c047e0b9ba092eda8d0d4392439e09d0f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "compact-model-space",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:2e9d6a12ad890dd7453e90c194c7fbbdd01dcda7851e5d16c2275427fa6dad74",
        "revision": 1,
        "sha256": "f6b51826d020b7289274f75e6c993c201217fb83c4e5feeb76f70453ffdeed7a"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "39a1ba115be76af003f1501ee04dbfc192fd71efa41bac6f357fe4f94fbc43ff"
      },
      "manuscript_sha256": "2f6cca4a5381109326012a1fa5e3b8329d73a9406986558fbfb1c939eadb7725",
      "guide_sha256": "c93c4e81fc73058260c1242a3134f2ef248dde9522190dec6e7344b892206124",
      "url": "../../cards/2e9d6a12ad890dd7453e90c194c7fbbdd01dcda7851e5d16c2275427fa6dad74/versions/gss-r1-39a1ba115be76af0/index.html",
      "card_json": "../../cards/2e9d6a12ad890dd7453e90c194c7fbbdd01dcda7851e5d16c2275427fa6dad74/versions/gss-r1-39a1ba115be76af0/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Ideal/MinimalIdealFamilyModel.lean.html?from=compact-model-space&start=170&end=172#L170",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/Ideal/MinimalIdealFamilyModel.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Ideal/MinimalIdealFamilyModel.lean",
        "raw_bytes": {
          "bytes": 16564,
          "sha256": "3c014dbe878f26cf4ccbee488070152a3462ceaee8a6592d71e4d7fb584cd9a4"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "14",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:2c9647786d7a86fe4fe7ffc8d30f26e964e04f65858a6915220629f7918072ba",
        "revision": 1,
        "sha256": "afe6051669975a09f5955926a5977589e99fda3baeb61e2ef598cfa502de43fa"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "3cc5b5cbc0d7b744754812157ed0e2507152288ce32ca8d834dbd2c4b308000e"
      },
      "manuscript_sha256": "8b94c4b0cb91d0a8a7429c16fdb69ce661b6b41093899bec4696f46c0458a5d6",
      "guide_sha256": "6c7623482e273bb0c542064653ebde6c3e6c549afe11c5b443835304a3afead8",
      "url": "../../cards/2c9647786d7a86fe4fe7ffc8d30f26e964e04f65858a6915220629f7918072ba/versions/gss-r1-3cc5b5cbc0d7b744/index.html",
      "card_json": "../../cards/2c9647786d7a86fe4fe7ffc8d30f26e964e04f65858a6915220629f7918072ba/versions/gss-r1-3cc5b5cbc0d7b744/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/FacialStructure/ExtremeMaximalFace.lean.html?from=14&start=102&end=111#L102",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/FacialStructure/ExtremeMaximalFace.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/FacialStructure/ExtremeMaximalFace.lean",
        "raw_bytes": {
          "bytes": 6411,
          "sha256": "b71a3818e32f9e26ac72a3e3f8de05a7be6e88c0897a509877ea85935c3e2805"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "4",
      "declaration": "NormedSpace.GeometricStructureSpace",
      "level": 1,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:2a268a095d051b4bcf9c934e4a60dea75d134e9a728ec7042cbb3f337410e13c",
        "revision": 1,
        "sha256": "5f6b1457045a74988a830333fcec541d63459263543911c3ad0be100b50a8ef7"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "bf1b0eb1ba8ddde084482ccc3351973dbf109ee34668774424eb4a1c00cf0ccf"
      },
      "manuscript_sha256": "6315fdbb173841f94e865ab87fd07bb8693b9fca792fdff8a8b52b98f2409921",
      "guide_sha256": "fc92c96e41dbf4a9cb9d3dcbe7d59ec7b0d017678bf572673b5e72f1fba620c9",
      "url": "../../cards/2a268a095d051b4bcf9c934e4a60dea75d134e9a728ec7042cbb3f337410e13c/versions/gss-r1-bf1b0eb1ba8ddde0/index.html",
      "card_json": "../../cards/2a268a095d051b4bcf9c934e4a60dea75d134e9a728ec7042cbb3f337410e13c/versions/gss-r1-bf1b0eb1ba8ddde0/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Face.lean.html?from=4&start=32&end=39#L32",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Face.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Face.lean",
        "raw_bytes": {
          "bytes": 1735,
          "sha256": "46ac614a9243e989d7e8ccc6bce4cee37fb8cc8420fdd0126a3f3befdf283743"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "13",
      "declaration": "ClosureSpace.IsLinkedSet",
      "level": 2,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:52e5d62f7053b8306fdbbac8b721e9ef0475b7afaf156c739fd2ab9294273625",
        "revision": 1,
        "sha256": "47fe06c79c7142605328ba71b49874f284d817485363590d00e8c5b78721dda9"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "74af612d52d19918f4bd3fb2ba6fbbe05c93721eb5e6f642ba929a20a909c88b"
      },
      "manuscript_sha256": "c1870d932256720edc702561c08b2909ceb7cbf858487e2194239a90e47b48b5",
      "guide_sha256": "194522cb23c6a88e903f0f677ac3d3a1a623fb8a8e7197c6be964e5882223aac",
      "url": "../../cards/52e5d62f7053b8306fdbbac8b721e9ef0475b7afaf156c739fd2ab9294273625/versions/gss-r1-74af612d52d19918/index.html",
      "card_json": "../../cards/52e5d62f7053b8306fdbbac8b721e9ef0475b7afaf156c739fd2ab9294273625/versions/gss-r1-74af612d52d19918/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/LinkedSet.lean.html?from=13&start=30&end=31#L30",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/LinkedSet.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/LinkedSet.lean",
        "raw_bytes": {
          "bytes": 3478,
          "sha256": "95ac973ca7bf940c90e63b9e3d8ae88e8279c316a8d6e21bf1200ffcae8c0533"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "8",
      "declaration": "ClosureSpace.component",
      "level": 2,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:7fd1342cdaa020367f7e436d83dd5b07f1709b2b3fce6d3fab51f8542192c8cb",
        "revision": 1,
        "sha256": "aaaf0ff06f46171ce6cfb9f4ef0b36221cad6a108f63cfc164c1b144ef32448d"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "c45fd4e9db692951694c24f4a25fceabc4185620c7681f3e93cfb14b1aa5fb19"
      },
      "manuscript_sha256": "b336a1963b23a667fa7a31fd8e649f005bf588d1577ec487467cbf89e437a14e",
      "guide_sha256": "3d84947b0f17529b6cc6f89034bc8f149817826404f1b008a5ea68acf61eeba3",
      "url": "../../cards/7fd1342cdaa020367f7e436d83dd5b07f1709b2b3fce6d3fab51f8542192c8cb/versions/gss-r1-c45fd4e9db692951/index.html",
      "card_json": "../../cards/7fd1342cdaa020367f7e436d83dd5b07f1709b2b3fce6d3fab51f8542192c8cb/versions/gss-r1-c45fd4e9db692951/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Components.lean.html?from=8&start=30&end=30#L30",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/Components.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/Components.lean",
        "raw_bytes": {
          "bytes": 5940,
          "sha256": "f8a603680a6aa871b86d4c994dcec4514d7470deadf9a60466e110a9f572fd4f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "compact-c0-sum-equivalence",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
      "level": 2,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:7f5a85e6d674d8d375ac4ebf6bfeaeeb5655656a613e9459b1e67a21d5902204",
        "revision": 1,
        "sha256": "e1e0e0d301a159bd19b4078791632050cf594d6c8101af190b2015a1cf208650"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "655f95229b7a0fdd67d156d04169105766d199f59d8a67eba46ca98570f8bd44"
      },
      "manuscript_sha256": "73df6d7ca97ed9c72f392965d991aedd2840e2dc3827d5beb80d9e9539a0d8db",
      "guide_sha256": "e6a00db83ba99d8101ff05902b5fa9e2c61e58ef57146986a55f482c7479fc2f",
      "url": "../../cards/7f5a85e6d674d8d375ac4ebf6bfeaeeb5655656a613e9459b1e67a21d5902204/versions/gss-r1-655f95229b7a0fdd/index.html",
      "card_json": "../../cards/7f5a85e6d674d8d375ac4ebf6bfeaeeb5655656a613e9459b1e67a21d5902204/versions/gss-r1-655f95229b7a0fdd/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/OrthogonalIdealCompactModel.lean.html?from=compact-c0-sum-equivalence&start=170&end=177#L170",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/OrthogonalIdealCompactModel.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/OrthogonalIdealCompactModel.lean",
        "raw_bytes": {
          "bytes": 14194,
          "sha256": "a5c99475d8487471e2c01a16fc3ab2977db8082b0e99a3f0f584c61d02caf7fe"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "16",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
      "level": 2,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:34a7bd4f9a44a5027e879e535d823650db9e1c88c189d9512f4abf807927b2b2",
        "revision": 1,
        "sha256": "083cb4f4e670eb0256e7e835b4056dc8792d6eb180de47bb6da5d2574fe82d66"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "0347c222eddf4f0482092c49e831c5718f0e6a8aff2aa038dfb23ba6974c5052"
      },
      "manuscript_sha256": "b7438a974654a3e6656f5cebd422b448daea612d6625f25511f4b9e88ac167b3",
      "guide_sha256": "eebbfb8175ae9fcbb844384656e9723c7698adb7e8ef67ee3d12269522a867c0",
      "url": "../../cards/34a7bd4f9a44a5027e879e535d823650db9e1c88c189d9512f4abf807927b2b2/versions/gss-r1-0347c222eddf4f04/index.html",
      "card_json": "../../cards/34a7bd4f9a44a5027e879e535d823650db9e1c88c189d9512f4abf807927b2b2/versions/gss-r1-0347c222eddf4f04/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ExtremeKernel.lean.html?from=16&start=49&end=65#L49",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ExtremeKernel.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ExtremeKernel.lean",
        "raw_bytes": {
          "bytes": 4409,
          "sha256": "ffb289a8aa48b8f8f1904fc4d11a079298429949a26fdf741078dac48ba94b0d"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "27",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
      "level": 2,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:4795f90dcc646f51bf6c591f133c4986f8f3694b72258db7a3f1ef7466c7ce4d",
        "revision": 1,
        "sha256": "8c34301154750a79af43401850d73ba22c2c5fabf40b6356c9a82b6cbdc77e18"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "e9e3247599f7b2969fe9fb008c0c08fc9ae976c0fcf1b99b2deb1ffc4f198f46"
      },
      "manuscript_sha256": "c6a6d504bcc53653894fa3c1128011d9e15bf4857d45c7ac3d32898f7a8d687d",
      "guide_sha256": "456e46394a0ff0fa8d0d6d84e036468d64a8d0a864d148ccd82dc83071c5e212",
      "url": "../../cards/4795f90dcc646f51bf6c591f133c4986f8f3694b72258db7a3f1ef7466c7ce4d/versions/gss-r1-e9e3247599f7b296/index.html",
      "card_json": "../../cards/4795f90dcc646f51bf6c591f133c4986f8f3694b72258db7a3f1ef7466c7ce4d/versions/gss-r1-e9e3247599f7b296/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPart.lean.html?from=27&start=35&end=38#L35",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPart.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPart.lean",
        "raw_bytes": {
          "bytes": 9858,
          "sha256": "0b735c8fddbf5a1bdc106b20c1a62a4eb3370b4c82366ad610bb1ea145b7aadc"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "5",
      "declaration": "NormedSpace.geometricStructureClosure",
      "level": 2,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:81027d4ce2fa25a93780f921f73b060bbfc8f9f580a00a9200face0fe00f60cc",
        "revision": 1,
        "sha256": "f0613532e38693386ec173bdb62889b7f8ec31170003f913143f4d5b730d09ff"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "cded7ac5dfdcacee2a082f86bc699d9ca4e8f7bc833b54c8936bc023fa9fa8e4"
      },
      "manuscript_sha256": "e63bf868032513bbcb2f6faa8dfa8aa3dca07a0a3a1a9a2e9ed1023a5bada9a1",
      "guide_sha256": "99389dbf27ede4fece97107f36df5d790b1234c0e0d34cf3876e405698bfb3ed",
      "url": "../../cards/81027d4ce2fa25a93780f921f73b060bbfc8f9f580a00a9200face0fe00f60cc/versions/gss-r1-cded7ac5dfdcacee/index.html",
      "card_json": "../../cards/81027d4ce2fa25a93780f921f73b060bbfc8f9f580a00a9200face0fe00f60cc/versions/gss-r1-cded7ac5dfdcacee/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Face.lean.html?from=5&start=32&end=39#L32",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Face.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Face.lean",
        "raw_bytes": {
          "bytes": 1735,
          "sha256": "46ac614a9243e989d7e8ccc6bce4cee37fb8cc8420fdd0126a3f3befdf283743"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "47",
      "declaration": "ClosureSpace.HasCompactOperatorHomeomorph",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:098d427d2201316055ccfe4ea61ab7733ae79857c7a734dfc892c6331c076008",
        "revision": 1,
        "sha256": "c632a03795d47f8b00e3a83382286052193bd94c8490f261c4650a59403bfd20"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "d0986f8f0a51799404cd33a885f642cae4b7cfdd57cffa4e9701fd6493141f38"
      },
      "manuscript_sha256": "18cdbac144ad5679e96b132b9a87ba0cd988a2628dd7761f868eb13617e3fc70",
      "guide_sha256": "b6a27c488f02593e1e7ce42445dbd2635ef015dd998b6fadb89bec16b107d388",
      "url": "../../cards/098d427d2201316055ccfe4ea61ab7733ae79857c7a734dfc892c6331c076008/versions/gss-r1-d0986f8f0a517994/index.html",
      "card_json": "../../cards/098d427d2201316055ccfe4ea61ab7733ae79857c7a734dfc892c6331c076008/versions/gss-r1-d0986f8f0a517994/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean.html?from=47&start=57&end=69#L57",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw_bytes": {
          "bytes": 16255,
          "sha256": "99db060f568a62d68d8f656cbe0ba8fe965f35f348b2c5755c8c503398a9fe12"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "46",
      "declaration": "ClosureSpace.HasContinuousFiniteCompactComparison",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:e3d1146d0e72a14eab872864b884e280adae5d387683e668928421e5dc6a02d1",
        "revision": 1,
        "sha256": "ca8f4799bd17ec868ce4f44d31ac34c0f24cd864efec072a98f81703e3793f5e"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "29dfdf789fe8e334b2d6867202f65d5d3a12d3f3f20bddec5277a5ca01e6a1a7"
      },
      "manuscript_sha256": "c4e9a71ce3f384da4b0ca892fb0dbe3a95d8a1b66efa09f9657ac0ac5b4742ff",
      "guide_sha256": "27746544e7a3d1b62a86f9e4669f511c8770dce72c312ccce61bbcf34ea57533",
      "url": "../../cards/e3d1146d0e72a14eab872864b884e280adae5d387683e668928421e5dc6a02d1/versions/gss-r1-29dfdf789fe8e334/index.html",
      "card_json": "../../cards/e3d1146d0e72a14eab872864b884e280adae5d387683e668928421e5dc6a02d1/versions/gss-r1-29dfdf789fe8e334/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean.html?from=46&start=39&end=53#L39",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw_bytes": {
          "bytes": 16255,
          "sha256": "99db060f568a62d68d8f656cbe0ba8fe965f35f348b2c5755c8c503398a9fe12"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "44",
      "declaration": "ClosureSpace.HasContinuousFiniteConjugation",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:6d987a777ad628da9151adcdfdef5693d121c754b214a7268d4bbb30b2b9677c",
        "revision": 1,
        "sha256": "358541b6d170193d39b233b293afdb208df3ebb6bc8c8237f451da19c80f1872"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "0f27ae46ebd2ea458f018e14d740f08a4705b8bccecaf312304824711e3d36e7"
      },
      "manuscript_sha256": "595afd17530ced6ecac85a269dea91694ea5ca0d00d7ce090c2f9de56737e9c6",
      "guide_sha256": "e3e74e8edcd77e6015afaf9b6d5ddbc3cb45b8aba5d847147a70feb2a3666001",
      "url": "../../cards/6d987a777ad628da9151adcdfdef5693d121c754b214a7268d4bbb30b2b9677c/versions/gss-r1-0f27ae46ebd2ea45/index.html",
      "card_json": "../../cards/6d987a777ad628da9151adcdfdef5693d121c754b214a7268d4bbb30b2b9677c/versions/gss-r1-0f27ae46ebd2ea45/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/FiniteConjugation.lean.html?from=44&start=41&end=50#L41",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Topology/ClosureSpace/FiniteConjugation.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Topology/ClosureSpace/FiniteConjugation.lean",
        "raw_bytes": {
          "bytes": 9507,
          "sha256": "126440acfc8b9ab99d6542226f150cbc4afc243def3b26724aa1b56843ba084d"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "48",
      "declaration": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:266063c05c13ee8c87329de652bb2c68fc5c83d3d4cbf55198ea6880fd333614",
        "revision": 1,
        "sha256": "fbc70107d55632b153fc3deadae96ddfab6f68d12e08812d321df2733bf7ea46"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "6758a52f2a940b62090076db4bd19c8b9b08d74814ec6001ee38ccecb66bec49"
      },
      "manuscript_sha256": "7879f6f0410157501255a514596fdcffed08837d96379171700cfe2316ae5d0f",
      "guide_sha256": "c11c87ae6a8aa5fb911f9217d27799c769eef98fafc6efed37a994863b756dda",
      "url": "../../cards/266063c05c13ee8c87329de652bb2c68fc5c83d3d4cbf55198ea6880fd333614/versions/gss-r1-6758a52f2a940b62/index.html",
      "card_json": "../../cards/266063c05c13ee8c87329de652bb2c68fc5c83d3d4cbf55198ea6880fd333614/versions/gss-r1-6758a52f2a940b62/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/HomogeneousCharacterization.lean.html?from=48&start=62&end=75#L62",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/HomogeneousCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/HomogeneousCharacterization.lean",
        "raw_bytes": {
          "bytes": 20780,
          "sha256": "406363ba4db6c6ca8d71f406abce0efe039a951f1bc7b538587d5223e411a0cf"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "57",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:968004a0ac46ed45e01dd56a9cc2b9cbc91621c8cf2606fa8f9ee3455c64f83c",
        "revision": 1,
        "sha256": "7217b4e6e4b56a65cb42a9a9d20d4734b2232eeb86cb13eda916b6715c02f556"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "f378386d28ad2284051ef38d9017e49f7a672fcd6e2094e6879d459ecab3ce95"
      },
      "manuscript_sha256": "f327e5cc9bd1451999b1cadb713c148a8dcb35e5707533941cebb59efe1d89f3",
      "guide_sha256": "b2b3708affbd3cfe731c44f6a950401cf637a5ed60e198552891e2c048a6b270",
      "url": "../../cards/968004a0ac46ed45e01dd56a9cc2b9cbc91621c8cf2606fa8f9ee3455c64f83c/versions/gss-r1-f378386d28ad2284/index.html",
      "card_json": "../../cards/968004a0ac46ed45e01dd56a9cc2b9cbc91621c8cf2606fa8f9ee3455c64f83c/versions/gss-r1-f378386d28ad2284/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/CompactlyRepresentedDecomposition.lean.html?from=57&start=67&end=79#L67",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/CompactlyRepresentedDecomposition.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/DirectSum/CompactlyRepresentedDecomposition.lean",
        "raw_bytes": {
          "bytes": 17106,
          "sha256": "8a5e2eb300ade64a3e3c0df4a15ff818b68058474056147750cc0261075ec0ee"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "19",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:cfac10adc682588763e2ae6326f6b0d05659d27f862faee2c7797548c83dff06",
        "revision": 1,
        "sha256": "ca3dfe8458bb62115cd3be45bf86612614c30c071c8c5eb316217185ac97d85f"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "e799bba24301220d422e1a4e0a927324c656968bf5a61c4627c48ff160d3a662"
      },
      "manuscript_sha256": "93672e6e84142a7f5560b54c9b5181a54a5c3dda8822d0aa1da5752baee06655",
      "guide_sha256": "95fe48b3c0caf5784d4c9d4c96629e8cded8c40fee08d93a396383f3dd8ee106",
      "url": "../../cards/cfac10adc682588763e2ae6326f6b0d05659d27f862faee2c7797548c83dff06/versions/gss-r1-e799bba24301220d/index.html",
      "card_json": "../../cards/cfac10adc682588763e2ae6326f6b0d05659d27f862faee2c7797548c83dff06/versions/gss-r1-e799bba24301220d/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/RepresentationComponents.lean.html?from=19&start=118&end=150#L118",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/RepresentationComponents.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/RepresentationComponents.lean",
        "raw_bytes": {
          "bytes": 10282,
          "sha256": "9cac5d69d9a1bc51788c41209c39c4db85d58c9250359a1ba822f279cb652de5"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "18",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:dc5425431b0c12bf15137e6002c16b5ba2c600bde91d02b23dd813e4369498d1",
        "revision": 1,
        "sha256": "84b21157565936f0900d773f331211a7db9ed29634a0b23ed30b85b3f84466c6"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "e6b09cd26ba001ea5f2d98b18444cf7ffb8a5e93cf23d6bc1372f2dd7d07b405"
      },
      "manuscript_sha256": "2003f1e785393ef4b8e1086293afd301319a515e2d470cd1236c5ac74ecfa348",
      "guide_sha256": "38c5ec8522c919948381b1d7c64ea56c8135f4b70f73f6be9655c5ba8415353f",
      "url": "../../cards/dc5425431b0c12bf15137e6002c16b5ba2c600bde91d02b23dd813e4369498d1/versions/gss-r1-e6b09cd26ba001ea/index.html",
      "card_json": "../../cards/dc5425431b0c12bf15137e6002c16b5ba2c600bde91d02b23dd813e4369498d1/versions/gss-r1-e6b09cd26ba001ea/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/RepresentationComponents.lean.html?from=18&start=104&end=113#L104",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/RepresentationComponents.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/RepresentationComponents.lean",
        "raw_bytes": {
          "bytes": 10282,
          "sha256": "9cac5d69d9a1bc51788c41209c39c4db85d58c9250359a1ba822f279cb652de5"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "32",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:5073fcc22c365d351ee496998fb6c996496d5cd2c983cfb21d4d847a74d4c04c",
        "revision": 1,
        "sha256": "fac51bc00375f43e8e70f91c7f937e7d5c6cf4bbc0d7d085d46c6df7c94f1c63"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "aefe0f2958a89d2b2b8fa24115247ad2443a44de8aac05a4154b1f645232e928"
      },
      "manuscript_sha256": "4f5d20cbfe8ee81540da514b21be3d3bc3fdbe5eabb982ec899d257c2bb193dc",
      "guide_sha256": "6406fef8981af6c93aa5663066d23ba8ac799adda4e8363993cbcff3f5b29a7d",
      "url": "../../cards/5073fcc22c365d351ee496998fb6c996496d5cd2c983cfb21d4d847a74d4c04c/versions/gss-r1-aefe0f2958a89d2b/index.html",
      "card_json": "../../cards/5073fcc22c365d351ee496998fb6c996496d5cd2c983cfb21d4d847a74d4c04c/versions/gss-r1-aefe0f2958a89d2b/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartBounded.lean.html?from=32&start=49&end=63#L49",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartBounded.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartBounded.lean",
        "raw_bytes": {
          "bytes": 11379,
          "sha256": "6200f945697aa6f7a5aa6a619c18c5121caf3b0bd1a9c6ef9991d70f98bf4e0e"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "31",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:a587d8854f5a92f1700294bc271b4ca2fce180c87fdbed8d1f5373a4a586cfec",
        "revision": 1,
        "sha256": "2e7550641addf5dff2d2a645d5101bdb8f3bac5631e92f4f64480dfc1e6c9665"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "0af56cd85a5c72ef8ecb328d1fffae1c9d0a77e2d0765a6e30da243911dbc870"
      },
      "manuscript_sha256": "01ac6d994cc5e3ade5f050476140b2be7f4b5625e001b7d03c359cc7a1fe71fa",
      "guide_sha256": "64a5a2eba3009fadb0f99026560300d174312d134810330d87d619f1bbb01717",
      "url": "../../cards/a587d8854f5a92f1700294bc271b4ca2fce180c87fdbed8d1f5373a4a586cfec/versions/gss-r1-0af56cd85a5c72ef/index.html",
      "card_json": "../../cards/a587d8854f5a92f1700294bc271b4ca2fce180c87fdbed8d1f5373a4a586cfec/versions/gss-r1-0af56cd85a5c72ef/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartBounded.lean.html?from=31&start=37&end=46#L37",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartBounded.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartBounded.lean",
        "raw_bytes": {
          "bytes": 11379,
          "sha256": "6200f945697aa6f7a5aa6a619c18c5121caf3b0bd1a9c6ef9991d70f98bf4e0e"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "17",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:1d5762922bae8477004705d3fdd85e6aedb3b9dafb54c41579a87ed1a2427fd6",
        "revision": 1,
        "sha256": "03b9952adb6d9fb262147afd2316953c3a702537714d16552bd4850595fd7416"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "f715bef56037c9e5b0ecc8d29f4cb5f4cf34b637de708c375f84ed44e66bd7cd"
      },
      "manuscript_sha256": "e098d2bcf7a8f43d380ee858377b654577687aa49fc4389d34f6a14224e807b2",
      "guide_sha256": "6557a20ff9782b48141e03b5bdf72da1ef39dd0bb1b93f2049bd3ec89737d7dc",
      "url": "../../cards/1d5762922bae8477004705d3fdd85e6aedb3b9dafb54c41579a87ed1a2427fd6/versions/gss-r1-f715bef56037c9e5/index.html",
      "card_json": "../../cards/1d5762922bae8477004705d3fdd85e6aedb3b9dafb54c41579a87ed1a2427fd6/versions/gss-r1-f715bef56037c9e5/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/PureStateKernel.lean.html?from=17&start=29&end=43#L29",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/PureStateKernel.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/PureStateKernel.lean",
        "raw_bytes": {
          "bytes": 3123,
          "sha256": "226eff4cdbd31f9a2efad7fad0bfc50571a26fd390a6e0e1ef769e0e95d1f848"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "33",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:a2705404d60633a46b0eb0b2efca80f869dcc0fbada6b1b4d355904be9334645",
        "revision": 1,
        "sha256": "0aebc56f5341ca9763e1361bb1e61e80f98231ce37b34dbde81b6b4631e86441"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "becbb62047a1942f88e457f4b6b6d5397d6b5a2bc1575162dc2da1546a30ea90"
      },
      "manuscript_sha256": "44f2a44ec02a3b79fc43efc0b2279dae2461cb1d7da452689aa237248c914b60",
      "guide_sha256": "2ba85634f9e0456d26fd9aae2be1954a007e9e7e396d414f96f0b7cd16134e58",
      "url": "../../cards/a2705404d60633a46b0eb0b2efca80f869dcc0fbada6b1b4d355904be9334645/versions/gss-r1-becbb62047a1942f/index.html",
      "card_json": "../../cards/a2705404d60633a46b0eb0b2efca80f869dcc0fbada6b1b4d355904be9334645/versions/gss-r1-becbb62047a1942f/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartLinked.lean.html?from=33&start=210&end=239#L210",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartLinked.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartLinked.lean",
        "raw_bytes": {
          "bytes": 12317,
          "sha256": "1fc2bac0d7ac52d9c22b7f4aed7f4e026aa2f4a6733b581fe156cfba409fefb6"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "29",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:3d7328185180155bea7c1880574a35b05bdae0c668b736859fa00b2169850f30",
        "revision": 1,
        "sha256": "03d2f93d3cea78fd6d4f61fd3eafe23c98319869c76b5e3df23095e03968c587"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "7357148c43380cb47dbf57e8df036f92bcef370c8ac2b3de0279e9f79668ebc6"
      },
      "manuscript_sha256": "890ace7736fe50b5993d5b425a14de2c52928700ba4c1c3ef5898d1018840b3d",
      "guide_sha256": "122091a640acd0f2e1fed2f09868263d07c383982992ff5544d79369aa472512",
      "url": "../../cards/3d7328185180155bea7c1880574a35b05bdae0c668b736859fa00b2169850f30/versions/gss-r1-7357148c43380cb4/index.html",
      "card_json": "../../cards/3d7328185180155bea7c1880574a35b05bdae0c668b736859fa00b2169850f30/versions/gss-r1-7357148c43380cb4/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartProjectivization.lean.html?from=29&start=77&end=83#L77",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartProjectivization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartProjectivization.lean",
        "raw_bytes": {
          "bytes": 8726,
          "sha256": "46047d7c85ac36f6ca13b63802b40aef083514680ac8f72f6f9f055bfab746fa"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "30",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:c5c807e60f29ab7e5c474f8feb345aefbfb09466fc16a5de659c5936369e3d47",
        "revision": 1,
        "sha256": "c325b049149172bc58d128cd561c0704128d711eec991ba945035ca4b254a325"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "1552e52c77e45972f9e4c65da3deb916a610b7c40c7c75b7e302627b026cc349"
      },
      "manuscript_sha256": "4144c7a479745a936261aac67f45df6952e184672e8a8c0c4f9304bbf5f5f195",
      "guide_sha256": "56c1abdb5efa40f61140d13784ff7d439cfb96137536accf6e4eb51d9b145c79",
      "url": "../../cards/c5c807e60f29ab7e5c474f8feb345aefbfb09466fc16a5de659c5936369e3d47/versions/gss-r1-1552e52c77e45972/index.html",
      "card_json": "../../cards/c5c807e60f29ab7e5c474f8feb345aefbfb09466fc16a5de659c5936369e3d47/versions/gss-r1-1552e52c77e45972/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinear.lean.html?from=30&start=178&end=188#L178",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinear.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinear.lean",
        "raw_bytes": {
          "bytes": 12328,
          "sha256": "f9f75f6bed8c946196666083063d70394cd05c6a8e54ae5689cc126da3054db9"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "9",
      "declaration": "NormedSpace.GeometricSpectrum",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:4939855a58535afd690c762d3c5eb2934d6675343e81f46879be683217621da5",
        "revision": 1,
        "sha256": "96ded6b59d6903074ee44899fe20a7ac843d71958e804834f2d3fdd59bba5918"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "b668cec6939db3b110a0ffecb33bde340624a0c2db09a6a2b5f1252beca5e721"
      },
      "manuscript_sha256": "073f26566ac963c3defe0e168017934cfc55a6f0186bc8955fc1de32edb21dd7",
      "guide_sha256": "25836e22e009de8389304326edab88561ab00238ad07718a78d3bd2d9ae704ac",
      "url": "../../cards/4939855a58535afd690c762d3c5eb2934d6675343e81f46879be683217621da5/versions/gss-r1-b668cec6939db3b1/index.html",
      "card_json": "../../cards/4939855a58535afd690c762d3c5eb2934d6675343e81f46879be683217621da5/versions/gss-r1-b668cec6939db3b1/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean.html?from=9&start=37&end=39#L37",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean",
        "raw_bytes": {
          "bytes": 3797,
          "sha256": "e2f688403bc22a66b6dd82ef04f99cdf0b0828537032c2b87fc917797827e6f8"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "10",
      "declaration": "NormedSpace.PrimitiveGeometricSpectrum",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:3b67671f8d00b7143cb622ec746b09b3ba0b6bcac0a8926d7154e3d863d5e910",
        "revision": 1,
        "sha256": "6cf916ad94d6be805ffb88ccafb30dbb5db4f547b6cbfaecfa97ac0cf8d48e41"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "6778bb277cbbd2514efea53559be1527c5bb502ec57fcf2f3e6c09b506d77d7f"
      },
      "manuscript_sha256": "7278b542293aa4e59167dc16d31beba42d95c4038a72ff189a67de6ae7f65b98",
      "guide_sha256": "732b1b11f00f5fd3b86852550612b867ac94383b90a018213741f41faed4d362",
      "url": "../../cards/3b67671f8d00b7143cb622ec746b09b3ba0b6bcac0a8926d7154e3d863d5e910/versions/gss-r1-6778bb277cbbd251/index.html",
      "card_json": "../../cards/3b67671f8d00b7143cb622ec746b09b3ba0b6bcac0a8926d7154e3d863d5e910/versions/gss-r1-6778bb277cbbd251/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean.html?from=10&start=37&end=39#L37",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean",
        "raw_bytes": {
          "bytes": 3797,
          "sha256": "e2f688403bc22a66b6dd82ef04f99cdf0b0828537032c2b87fc917797827e6f8"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "6",
      "declaration": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
      "level": 3,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:e7204a2011082aa580b29d7ccd62e08ddd52aca1e2c46b67039f4c16541c0930",
        "revision": 1,
        "sha256": "1c28567ab50d56a6375241e486873100c5e40573e93d09a82158d0f7e5e2aea6"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "25b7fa4b40b8bc832d3399521fface99e438f556c5eaed0a8fcbfa5a7fd34a09"
      },
      "manuscript_sha256": "67adbc830f95e6c41ac7744bd0bbc1750cbf465c8d6ef76ccbc31b20b3059a1d",
      "guide_sha256": "800d88993aa2458480a3ec860de406f63e1e3d155af811da52bc68816d93f439",
      "url": "../../cards/e7204a2011082aa580b29d7ccd62e08ddd52aca1e2c46b67039f4c16541c0930/versions/gss-r1-25b7fa4b40b8bc83/index.html",
      "card_json": "../../cards/e7204a2011082aa580b29d7ccd62e08ddd52aca1e2c46b67039f4c16541c0930/versions/gss-r1-25b7fa4b40b8bc83/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Preserver.lean.html?from=6&start=151&end=156#L151",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Preserver.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Preserver.lean",
        "raw_bytes": {
          "bytes": 6919,
          "sha256": "97cb58d68e8177eb69ab7ceb039970b127ea71bf99915985d891c41567e4bcb8"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "55",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:e1f8ae266d1290e2e7415612fea378e3069c91635f644d58b6b26f1a0eafeef4",
        "revision": 1,
        "sha256": "15df9af01fb55a1bf3c91e399859630f7d80140dc5895327aa800161875df428"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "2e5669e8d2c4946450867b5d0fceac63dc631c63e7570ce892d372812416a5a6"
      },
      "manuscript_sha256": "7a355b471983ef09468f8745567a53d15550271782535a481842f99c78932eae",
      "guide_sha256": "3076349523c488b9161fe05fbd89e798cded568014a349be5f53baa21503afc5",
      "url": "../../cards/e1f8ae266d1290e2e7415612fea378e3069c91635f644d58b6b26f1a0eafeef4/versions/gss-r1-2e5669e8d2c49464/index.html",
      "card_json": "../../cards/e1f8ae266d1290e2e7415612fea378e3069c91635f644d58b6b26f1a0eafeef4/versions/gss-r1-2e5669e8d2c49464/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/CompactRepresentationCharacterization.lean.html?from=55&start=142&end=156#L142",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/CompactRepresentationCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/CompactRepresentationCharacterization.lean",
        "raw_bytes": {
          "bytes": 10242,
          "sha256": "df336d80fa66ba38ebcb4965196e85d9b19bfc390ebb1d2918f720d7ca9c006f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "25",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:5429bab04d4f40f5c73221227780b415fefa1d60201f14325eccecbba2b19ca0",
        "revision": 1,
        "sha256": "09f468e537a19e3fd2250e8613f42ba608e197b112a76f487c02f4f1cc471bd2"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "88b7da14af528988d3da4840bff2cad7782ca2b3b0f0143035a5b0bd67fc219f"
      },
      "manuscript_sha256": "d15486aeb4279521b5dcdfb471bad57e7be44f92e9ba4eb8673a5326b8d38bd3",
      "guide_sha256": "dc28d811385cb97984a60bb22a2012e7fcc566ef4b782ee65f27a9ea067a84a8",
      "url": "../../cards/5429bab04d4f40f5c73221227780b415fefa1d60201f14325eccecbba2b19ca0/versions/gss-r1-88b7da14af528988/index.html",
      "card_json": "../../cards/5429bab04d4f40f5c73221227780b415fefa1d60201f14325eccecbba2b19ca0/versions/gss-r1-88b7da14af528988/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ImageSubspace.lean.html?from=25&start=62&end=96#L62",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ImageSubspace.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ImageSubspace.lean",
        "raw_bytes": {
          "bytes": 9692,
          "sha256": "9c3a311326b0139909454fe8d62c1d8d497ae7975dbdcd02ec407bda025b1324"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "56",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:ae080d5891f10f5b129063951765313149d728fd1adffd820c33396a9641b794",
        "revision": 1,
        "sha256": "0033e9b963ed3fa45f0191a1c1dab8c5c97858ccef83def82f74557af837493d"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "ea91a963dc22dec8d98eead336ee113ed0ce54b2f431cf062f2a75c84bdda1bf"
      },
      "manuscript_sha256": "bf4a800f995b03a64c00930eeb5b59209410f43369d0cde8312c5c6c2b36a212",
      "guide_sha256": "45ba1b4aeabf382bb54b8e06692982d3db18a662b800438df3dc29a204a4755e",
      "url": "../../cards/ae080d5891f10f5b129063951765313149d728fd1adffd820c33396a9641b794/versions/gss-r1-ea91a963dc22dec8/index.html",
      "card_json": "../../cards/ae080d5891f10f5b129063951765313149d728fd1adffd820c33396a9641b794/versions/gss-r1-ea91a963dc22dec8/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/CompactRepresentationCharacterization.lean.html?from=56&start=167&end=196#L167",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/CompactRepresentationCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/Spectrum/CompactRepresentationCharacterization.lean",
        "raw_bytes": {
          "bytes": 10242,
          "sha256": "df336d80fa66ba38ebcb4965196e85d9b19bfc390ebb1d2918f720d7ca9c006f"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "28",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:59104afef875e8e638fb7e2aab8b9911f46750d7596282da822dfc7c2d4e91cb",
        "revision": 1,
        "sha256": "5edd3ba38be38cbf4255c4f24ed83518cb6adddd2e72969f36a6ea7dd64a8a61"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "be2c9f197ae2181f4a510a80e1923f237ee410527e93866766b689397438a330"
      },
      "manuscript_sha256": "6de0837dbdef18067bb20a59763924c37000c7aa607df20da86eff2ae94df880",
      "guide_sha256": "c8c32698ccb805bb63cc27ab16f50bfd29ec5d39aebe6970a7a080f8a9a30351",
      "url": "../../cards/59104afef875e8e638fb7e2aab8b9911f46750d7596282da822dfc7c2d4e91cb/versions/gss-r1-be2c9f197ae2181f/index.html",
      "card_json": "../../cards/59104afef875e8e638fb7e2aab8b9911f46750d7596282da822dfc7c2d4e91cb/versions/gss-r1-be2c9f197ae2181f/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPart.lean.html?from=28&start=96&end=118#L96",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPart.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPart.lean",
        "raw_bytes": {
          "bytes": 9858,
          "sha256": "0b735c8fddbf5a1bdc106b20c1a62a4eb3370b4c82366ad610bb1ea145b7aadc"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "20",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:bd23b958c2bb8d456d73377db09ea107d5de98389ab34d3c93a173d0ce58a06c",
        "revision": 1,
        "sha256": "76d14678ffc54ce1940dd1698202d4ed65c82570afc906e4527a3a707439ea98"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "fb2eb7faae06898e374a9ba6521bbbd93ac1aafe1269c6616e008ce863e3455f"
      },
      "manuscript_sha256": "ca59a64f25815344ff40a0fdd49d55a006446ca261bc87e57761a99e33695df3",
      "guide_sha256": "ac93165b78534cc567b760f3ce28f08d70436a2b9600d984602c3993871dd24d",
      "url": "../../cards/bd23b958c2bb8d456d73377db09ea107d5de98389ab34d3c93a173d0ce58a06c/versions/gss-r1-fb2eb7faae06898e/index.html",
      "card_json": "../../cards/bd23b958c2bb8d456d73377db09ea107d5de98389ab34d3c93a173d0ce58a06c/versions/gss-r1-fb2eb7faae06898e/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/AbsoluteState.lean.html?from=20&start=234&end=239#L234",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/AbsoluteState.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/AbsoluteState.lean",
        "raw_bytes": {
          "bytes": 17775,
          "sha256": "afe0569cd3868a0a6f245eaa7c781ba52db87401c1334a3deeac9ad74ee939ec"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "36",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:5cfbc37ef11004746da196fbfc5f5056fde9ac47956927ce62f2432455f19e67",
        "revision": 1,
        "sha256": "0ddef056429142f025bf5d82af0ca43d5ca635b8ae7563922eaddccbcdf7ae3f"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "ba829240898e4fb05ee8f2b7aa4e396f3596736f1a4c438d0499b0c69f0eb509"
      },
      "manuscript_sha256": "f12e8652c092a63ce9d3079367c698f63661ce67a1bdfdb9b51fd8a4862befc1",
      "guide_sha256": "37361df04d8031869e5490c83bb1f3c0687fe150a7edf5e6f8e23a784bdb1873",
      "url": "../../cards/5cfbc37ef11004746da196fbfc5f5056fde9ac47956927ce62f2432455f19e67/versions/gss-r1-ba829240898e4fb0/index.html",
      "card_json": "../../cards/5cfbc37ef11004746da196fbfc5f5056fde9ac47956927ce62f2432455f19e67/versions/gss-r1-ba829240898e4fb0/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartProjectiveDimension.lean.html?from=36&start=215&end=221#L215",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartProjectiveDimension.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartProjectiveDimension.lean",
        "raw_bytes": {
          "bytes": 12462,
          "sha256": "95244508917b8dc2e60a36b1687f7e3b6bb0c9cdb710f2a42b27c314e57c6c82"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "34",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:ff830108100bff4a506917dc761a7cb66c608fdf5458f297ea9004c43c6b0d0c",
        "revision": 1,
        "sha256": "53ddb1eeb700070874ff179acdd3430fc9c53ce664d90854f331aa6d0dceef64"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "f9968bc86c07e5d7e0a6f617e78f7fbcd4485c964d3a856f22419148ecbfef4c"
      },
      "manuscript_sha256": "e1b050edf4dff7a8fb0ae08438d2bd110742370a7728e95760383a142477eaba",
      "guide_sha256": "3be10a9c29a7031d356e18dcbacc2efe36b083b3861e0d6b63e77043027d6ca1",
      "url": "../../cards/ff830108100bff4a506917dc761a7cb66c608fdf5458f297ea9004c43c6b0d0c/versions/gss-r1-f9968bc86c07e5d7/index.html",
      "card_json": "../../cards/ff830108100bff4a506917dc761a7cb66c608fdf5458f297ea9004c43c6b0d0c/versions/gss-r1-f9968bc86c07e5d7/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartLinkedSet.lean.html?from=34&start=178&end=205#L178",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartLinkedSet.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartLinkedSet.lean",
        "raw_bytes": {
          "bytes": 12476,
          "sha256": "671f38a67d1ad7de598fad1c68516ce877514474efea11e557f00c429200c957"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "37",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:cdd4d1e9b1d3b5f4a4aa6965aec3cbfa46729e85fb8dce6f7924c8c8291a0407",
        "revision": 1,
        "sha256": "1919ef0db13fddc618e9b733a7d233cfee2fe799b7c0efdaf7bca67e87358756"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "4d7edc5c00bc315d2b47213dbfff1c440829740754b2a7d0d76f8cb2c641d5c9"
      },
      "manuscript_sha256": "2b8d132142726e8075ff2005a04d21cefc0e6f719845bc7656719afcea38f504",
      "guide_sha256": "a773ebb94ea9d68a2c31a3635df37a3495bda4bafc25b604feabbbf5ae1e0f27",
      "url": "../../cards/cdd4d1e9b1d3b5f4a4aa6965aec3cbfa46729e85fb8dce6f7924c8c8291a0407/versions/gss-r1-4d7edc5c00bc315d/index.html",
      "card_json": "../../cards/cdd4d1e9b1d3b5f4a4aa6965aec3cbfa46729e85fb8dce6f7924c8c8291a0407/versions/gss-r1-4d7edc5c00bc315d/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRealization.lean.html?from=37&start=179&end=225#L179",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRealization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRealization.lean",
        "raw_bytes": {
          "bytes": 15458,
          "sha256": "a38463667b8a521fb7e214a79428b8f1423c4eef833c85400643beec241b2b7a"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "11",
      "declaration": "NormedSpace.geometricSpectrumToPrimitive",
      "level": 4,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:688c258fc54eb4a15918062a1e2948443b810613bbaadc07bf715c20a04aa429",
        "revision": 1,
        "sha256": "1881643031f1cb9a6c89f26c7e4b9535f4f8a9b2411d2e11505608edd8a4ad80"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "1ade8901e862180aa879dc0a6b4f5d59b71cb2d96c1175cf38b87e8c4bcf5c0e"
      },
      "manuscript_sha256": "d748c166c9236979efa92a11471c961308169b56bbcdf2406fabe48365c6857d",
      "guide_sha256": "20bb343d6629ee4e7cba5d4dfc52e1059f4f2e90e0327904a4937d16d515961e",
      "url": "../../cards/688c258fc54eb4a15918062a1e2948443b810613bbaadc07bf715c20a04aa429/versions/gss-r1-1ade8901e862180a/index.html",
      "card_json": "../../cards/688c258fc54eb4a15918062a1e2948443b810613bbaadc07bf715c20a04aa429/versions/gss-r1-1ade8901e862180a/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean.html?from=11&start=37&end=39#L37",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/Normed/GeometricStructure/Basic.lean",
        "raw_bytes": {
          "bytes": 3797,
          "sha256": "e2f688403bc22a66b6dd82ef04f99cdf0b0828537032c2b87fc917797827e6f8"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "53",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
      "level": 5,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:166b5d638f6c27a451035ece7780b33266836361fcf44befbf47db1e236d2049",
        "revision": 1,
        "sha256": "9d4d6588039e85d4d272c23dae376a4b6f1af61fc2d18f9306d4ad0f84852e86"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "d97e88f2c1de3824c23b4eb8ee4032919adf43e791de44518b07a1fc3869a11e"
      },
      "manuscript_sha256": "46a5a97cc6a50f3148398b92b66c435c513e9ef2c258c90dd162f7d8caf83e3c",
      "guide_sha256": "59308268c7e72d2f3ccaa9eb2e5471f7d72ec1f5b5e041adda9a6422e35474ba",
      "url": "../../cards/166b5d638f6c27a451035ece7780b33266836361fcf44befbf47db1e236d2049/versions/gss-r1-d97e88f2c1de3824/index.html",
      "card_json": "../../cards/166b5d638f6c27a451035ece7780b33266836361fcf44befbf47db1e236d2049/versions/gss-r1-d97e88f2c1de3824/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/FaithfulNormalPart.lean.html?from=53&start=200&end=236#L200",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/FaithfulNormalPart.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/FaithfulNormalPart.lean",
        "raw_bytes": {
          "bytes": 12992,
          "sha256": "23ce4f23a554d629596348f5647c60d1aae9de3e08cc823d8efd820179efa3e9"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "21",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
      "level": 5,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:407f570c29b53ad2e9ffa1b46613c142a0e8c631c2aca03ec172505aade4b777",
        "revision": 1,
        "sha256": "99b03276d4086a853abc410087669c306af2d6c766e60eedcb6bee188c8a057b"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "6167c2d975ac02b4155f91c88b1a8a6775a6b75e49d568431f6dabccc5399ace"
      },
      "manuscript_sha256": "964b5ca961e42940c244e402d89766a54b832c8a601d109d14e086705f0943b4",
      "guide_sha256": "76c41a988e49227e2a562409fedafc5c59e9755d1d7898e125c9a5243985bec5",
      "url": "../../cards/407f570c29b53ad2e9ffa1b46613c142a0e8c631c2aca03ec172505aade4b777/versions/gss-r1-6167c2d975ac02b4/index.html",
      "card_json": "../../cards/407f570c29b53ad2e9ffa1b46613c142a0e8c631c2aca03ec172505aade4b777/versions/gss-r1-6167c2d975ac02b4/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/AbsoluteState.lean.html?from=21&start=281&end=294#L281",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/AbsoluteState.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/AbsoluteState.lean",
        "raw_bytes": {
          "bytes": 17775,
          "sha256": "afe0569cd3868a0a6f245eaa7c781ba52db87401c1334a3deeac9ad74ee939ec"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "42",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
      "level": 5,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:268b26f75aec1f93a1d7f03336590d46085719c35a97ca1c519b727608731e0c",
        "revision": 1,
        "sha256": "c28c63e9af346265d56ae05fd4412c3dbcfc893dd5b8e4e9a8746c0b3daf7959"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "09052d98b151adfac1f861cbe3646ff26ed149c5f928fbe1f3123faa50c6a1b3"
      },
      "manuscript_sha256": "56886c45bc5966c2b6f456a684f93e65b6c8d88da20928d419fbe0149abd22d7",
      "guide_sha256": "c4e4fd0e1b6ceb745e9eab7536ae5a5877f23c80a7f67e2ec679c7b2a333ee7c",
      "url": "../../cards/268b26f75aec1f93a1d7f03336590d46085719c35a97ca1c519b727608731e0c/versions/gss-r1-09052d98b151adfa/index.html",
      "card_json": "../../cards/268b26f75aec1f93a1d7f03336590d46085719c35a97ca1c519b727608731e0c/versions/gss-r1-09052d98b151adfa/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartHilbertDimension.lean.html?from=42&start=66&end=79#L66",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartHilbertDimension.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartHilbertDimension.lean",
        "raw_bytes": {
          "bytes": 4797,
          "sha256": "3f25e157626fa51a4588c227393195d920456ff635bb85bf526d24ac9f5fd38b"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "40",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
      "level": 5,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:dea300e85441947834f53ac22636686acdcbc75b0e3128604dabf8cbaa7fd024",
        "revision": 1,
        "sha256": "be1f8a7e519abd29afde1cabde352d09fcf8cada665a77f96ad75d184b69dc00"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "a8369a09aa88208eb12ffcc7404922f747430c00ad355e780cbc1da79b655971"
      },
      "manuscript_sha256": "b17078a1fb58dce51f2bd2265da558293607c9a2ee8ce13d855153d913700112",
      "guide_sha256": "20f425e06820b809354059763dd5e230cb3b736309fd7f80ae7ffc273a41f262",
      "url": "../../cards/dea300e85441947834f53ac22636686acdcbc75b0e3128604dabf8cbaa7fd024/versions/gss-r1-a8369a09aa88208e/index.html",
      "card_json": "../../cards/dea300e85441947834f53ac22636686acdcbc75b0e3128604dabf8cbaa7fd024/versions/gss-r1-a8369a09aa88208e/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRegularity.lean.html?from=40&start=238&end=246#L238",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRegularity.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRegularity.lean",
        "raw_bytes": {
          "bytes": 12407,
          "sha256": "e1c3c617c7a1966d78e01e4832dd8dbfef300f907a1ee02a70da2800b36ec543"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "39",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
      "level": 5,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:fc684fc1b5cbdec020a888573ebda515b74803f00dac5a45c2f2451e93c3030a",
        "revision": 1,
        "sha256": "5747ac02d646c1376a8ac59c2b44dd537d85973255ec9801b297aabc69238fb9"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "ea876dbc73dca7ca93cebec01fd27c86b328a62af733f7babd4efd4d551579bd"
      },
      "manuscript_sha256": "e9719c6263686fc15f38a4a299239a5dc7cb90c4116c77b82bd2d2e919f09d60",
      "guide_sha256": "b95a048e86d2930176e56eeac754f6af16adaf32fa04b016d44019613f4341be",
      "url": "../../cards/fc684fc1b5cbdec020a888573ebda515b74803f00dac5a45c2f2451e93c3030a/versions/gss-r1-ea876dbc73dca7ca/index.html",
      "card_json": "../../cards/fc684fc1b5cbdec020a888573ebda515b74803f00dac5a45c2f2451e93c3030a/versions/gss-r1-ea876dbc73dca7ca/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRegularity.lean.html?from=39&start=229&end=235#L229",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRegularity.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartSemilinearRegularity.lean",
        "raw_bytes": {
          "bytes": 12407,
          "sha256": "e1c3c617c7a1966d78e01e4832dd8dbfef300f907a1ee02a70da2800b36ec543"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "41",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
      "level": 6,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:8686551592dd8150c7ef5068bf8d05af2e6bdb9ead5db503d7a630dfd196a5ee",
        "revision": 1,
        "sha256": "72d5d31fa3ffa85e12fbee97141330befc8cbcafeb8a18eff6cc05f6d3421860"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "7f7f848863859418d15fd4bdf820dbd977715d7f5de13c5a9dbd05c90eb26716"
      },
      "manuscript_sha256": "f56d9834a07ff308591b812216e342a9cb8846ef79066cc93b63a84cc87a160a",
      "guide_sha256": "83e5b805af3474a34825245c2e120f89f35e38d3e511ee3f1278af918539f9ec",
      "url": "../../cards/8686551592dd8150c7ef5068bf8d05af2e6bdb9ead5db503d7a630dfd196a5ee/versions/gss-r1-7f7f848863859418/index.html",
      "card_json": "../../cards/8686551592dd8150c7ef5068bf8d05af2e6bdb9ead5db503d7a630dfd196a5ee/versions/gss-r1-7f7f848863859418/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartClassificationConsequences.lean.html?from=41&start=328&end=429#L328",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartClassificationConsequences.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/NormalPartClassificationConsequences.lean",
        "raw_bytes": {
          "bytes": 26016,
          "sha256": "28637d84361ab497d6f89ca76c5edb62562a0db2d5582e36a8a6dc41b5219525"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "22",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
      "level": 6,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:0b334e5bbbc829b14a2ca71c55edf8f4023aabf84d325141773156b8cb7305fb",
        "revision": 1,
        "sha256": "34e000fcce21325dbe5229f4ca9cbc22a9ec49d4470685a125077df4dc02bf4f"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "066cbd252414e7394a1d6fff819d7f3380ee46882bc564d67017edcc339b29b9"
      },
      "manuscript_sha256": "929d7eb4d80cc18286a6c57cc3493480eed463b0fd0eb5758cf5b75e6d7e7570",
      "guide_sha256": "6da7c1eaa72180eafbb69a024742b0f7bbf90a70b28b8856ab89a2eddce686db",
      "url": "../../cards/0b334e5bbbc829b14a2ca71c55edf8f4023aabf84d325141773156b8cb7305fb/versions/gss-r1-066cbd252414e739/index.html",
      "card_json": "../../cards/0b334e5bbbc829b14a2ca71c55edf8f4023aabf84d325141773156b8cb7305fb/versions/gss-r1-066cbd252414e739/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralComparison.lean.html?from=22&start=142&end=159#L142",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralComparison.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralComparison.lean",
        "raw_bytes": {
          "bytes": 9852,
          "sha256": "87284c91d73f596a13fe051d81c68a5635cba32fe694db952955e5bfefed1a32"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "24",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
      "level": 7,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:b5a192e841f43aae6cbba4d6140d4b7da715805946eec19acd5e5cbaa90a8573",
        "revision": 1,
        "sha256": "afe60da871ed0e1467395b9d1f9d26c757ba308db45536bf90d19691ab51488d"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "2acfa649372da9c71ee03315232340169e10cfa4d8c367d90361d922a0b85a5f"
      },
      "manuscript_sha256": "b340191e921b593a1d0ee6c011d55affbbedb6a6c26679db54f2f1e2e15ef644",
      "guide_sha256": "42fc609488ecb57e9b3b6c1e8cfd536aa1767b747a9d293aa88ee1cce10ce801",
      "url": "../../cards/b5a192e841f43aae6cbba4d6140d4b7da715805946eec19acd5e5cbaa90a8573/versions/gss-r1-2acfa649372da9c7/index.html",
      "card_json": "../../cards/b5a192e841f43aae6cbba4d6140d4b7da715805946eec19acd5e5cbaa90a8573/versions/gss-r1-2acfa649372da9c7/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralHomeomorph.lean.html?from=24&start=136&end=142#L136",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralHomeomorph.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralHomeomorph.lean",
        "raw_bytes": {
          "bytes": 8826,
          "sha256": "f92134dfd4ba015043177fd159bff9905179506d30877e5af3cf38eaf71c6237"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "23",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
      "level": 7,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:32a0d85ad11505691601ed6ff3a2592463049e23dac1307583b72fb7d89f4fe5",
        "revision": 1,
        "sha256": "a4d7edd8e108c13c9ed4157e3b7b5bf17a0b06296ba9c79e7d99c6e8ecf168cd"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "f413a6b2f988d5e713fc49f95581364ba8df600f97607e0fb9b054c72ecc4d85"
      },
      "manuscript_sha256": "5456e61c8b93c8aee0e268aa5a14cfd141b090aa1fe575f91bd2ecb0f6ab2355",
      "guide_sha256": "cbe320016c25bb0736fe0f71919e21039d6baf86aae95d837cf100636f63b707",
      "url": "../../cards/32a0d85ad11505691601ed6ff3a2592463049e23dac1307583b72fb7d89f4fe5/versions/gss-r1-f413a6b2f988d5e7/index.html",
      "card_json": "../../cards/32a0d85ad11505691601ed6ff3a2592463049e23dac1307583b72fb7d89f4fe5/versions/gss-r1-f413a6b2f988d5e7/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralHomeomorph.lean.html?from=23&start=128&end=133#L128",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralHomeomorph.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralHomeomorph.lean",
        "raw_bytes": {
          "bytes": 8826,
          "sha256": "f92134dfd4ba015043177fd159bff9905179506d30877e5af3cf38eaf71c6237"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "54",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:f66f28a81e5b11fe946b7764a17aeab00b86335eca4620bd782d6ae3a0378354",
        "revision": 1,
        "sha256": "ed9e970b2ecd6c7edc02f6d75d85299f9f410338e661f957ed03b3daa2e87f52"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "df7d71195145f58b0192cc02f22644b32ec4ef391e913e5c9fc514a6b678a1e5"
      },
      "manuscript_sha256": "6f0f1f134f7b7fe0e13705251dcc39b4ba2521f78b9f4e5f2172f8121b3f7cdf",
      "guide_sha256": "68322df4ad3867fec8b47223181278231c25cd4ecad4d94cef5bb75f840c509c",
      "url": "../../cards/f66f28a81e5b11fe946b7764a17aeab00b86335eca4620bd782d6ae3a0378354/versions/gss-r1-df7d71195145f58b/index.html",
      "card_json": "../../cards/f66f28a81e5b11fe946b7764a17aeab00b86335eca4620bd782d6ae3a0378354/versions/gss-r1-df7d71195145f58b/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/CompactTrichotomyTransport.lean.html?from=54&start=430&end=443#L430",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/CompactTrichotomyTransport.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/CompactTrichotomyTransport.lean",
        "raw_bytes": {
          "bytes": 23927,
          "sha256": "d03a54b6ea031cecce1787c6924bcbc5a786cec83dbc053b4ed4cc3390249e84"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "43",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:1b53fbcb51ead52ce115008da9983e5c60906f86e1ee22c73fd5f7506b298524",
        "revision": 1,
        "sha256": "70a1e3fb7fa315825f812a08558a8cc86b7e755d1062da2c3ac75a9f04d7cb00"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "e50e61ed10aff89df9a9efd4fc014f766b2596e96943d16677a32bc3dcf0360e"
      },
      "manuscript_sha256": "482bc886dbd0ce1fa7c43be8502adaaf7e2426c68f610547fdef2280e3add312",
      "guide_sha256": "00b3c7f54bf0c221bfb12d2abfa9a40ce436fd8596a46a8882da0fb746ec647b",
      "url": "../../cards/1b53fbcb51ead52ce115008da9983e5c60906f86e1ee22c73fd5f7506b298524/versions/gss-r1-e50e61ed10aff89d/index.html",
      "card_json": "../../cards/1b53fbcb51ead52ce115008da9983e5c60906f86e1ee22c73fd5f7506b298524/versions/gss-r1-e50e61ed10aff89d/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectrumSingleton.lean.html?from=43&start=190&end=213#L190",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectrumSingleton.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectrumSingleton.lean",
        "raw_bytes": {
          "bytes": 10989,
          "sha256": "8cdb41bafe624674f45c31e2b07dd6d18ccd4b24fd28a2fa649ef0fc30779c26"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "45",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:dc51710ade94e76e70bcb7900241f80803b3dce6e116bf506bc4edf74a6b2656",
        "revision": 1,
        "sha256": "a7b2ab68a35d5f1323865d88f3d9b31b578106c0b10f141e1e18631bc910ddbe"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "d6d5c51df5128d1a311056d8ad238ea1d5bf5364098dbfd6bd04efe83f3c5f32"
      },
      "manuscript_sha256": "b97ca9ba48a7757d123ccaf5eb5ebd4009a5f09b5123a99bbec8e8a34fdb35f9",
      "guide_sha256": "ecc0f9fd68a85c55440fa4b51e1ee4e5e255f4c1d4dcf1a0fa1e82e15e233ad2",
      "url": "../../cards/dc51710ade94e76e70bcb7900241f80803b3dce6e116bf506bc4edf74a6b2656/versions/gss-r1-d6d5c51df5128d1a/index.html",
      "card_json": "../../cards/dc51710ade94e76e70bcb7900241f80803b3dce6e116bf506bc4edf74a6b2656/versions/gss-r1-d6d5c51df5128d1a/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryCharacterization.lean.html?from=45&start=85&end=104#L85",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryCharacterization.lean",
        "raw_bytes": {
          "bytes": 8246,
          "sha256": "67cb7582818fcc372a4a83ec0de41be107f660ea1e2670e07d0fdf8b0cfff5df"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "49",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:8dd97c9c7d665daf08abe024f5cd919ea304bee73fb0cd0f717abdb093598267",
        "revision": 1,
        "sha256": "f47d232fe5ba3eaf3cf6c2bcc996326b68e2b4d249384f079b2e936c15e36800"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "391d3e0bdbda498b611cc1126163434e494678d0042e3a7127b1a9db36f3803c"
      },
      "manuscript_sha256": "ad4f6377974bcef75a89965950f9b1b08781d283a9a6f4302aee47422ae078fe",
      "guide_sha256": "dc0cc9f8e9559feb1da8a5c350dbaf2129759df8a7b38fd09dd726493acb5649",
      "url": "../../cards/8dd97c9c7d665daf08abe024f5cd919ea304bee73fb0cd0f717abdb093598267/versions/gss-r1-391d3e0bdbda498b/index.html",
      "card_json": "../../cards/8dd97c9c7d665daf08abe024f5cd919ea304bee73fb0cd0f717abdb093598267/versions/gss-r1-391d3e0bdbda498b/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean.html?from=49&start=228&end=242#L228",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw_bytes": {
          "bytes": 16255,
          "sha256": "99db060f568a62d68d8f656cbe0ba8fe965f35f348b2c5755c8c503398a9fe12"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "51",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:ac0a3be2c564732508d8ad691f5b3cc689bc54b939dea39024556786433cfa9c",
        "revision": 1,
        "sha256": "ab86a6a8343db6b80c531bf0e80f5ac7b169c8d6d0ff6142668a0a529f4594c3"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "6ce5df88ae9d6bba73799c0572dae7919fc8d437cdece5e5dfb36667ece171a4"
      },
      "manuscript_sha256": "d350eb3cdf6d39b38c3ea70836986b7a9f34089bba2bdf72394f0b930e4dfae2",
      "guide_sha256": "496b8998b11c786383821d6e52e2b7543b6764d09377beb07e010384493e874e",
      "url": "../../cards/ac0a3be2c564732508d8ad691f5b3cc689bc54b939dea39024556786433cfa9c/versions/gss-r1-6ce5df88ae9d6bba/index.html",
      "card_json": "../../cards/ac0a3be2c564732508d8ad691f5b3cc689bc54b939dea39024556786433cfa9c/versions/gss-r1-6ce5df88ae9d6bba/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/HomogeneousCharacterization.lean.html?from=51&start=373&end=381#L373",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/HomogeneousCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/HomogeneousCharacterization.lean",
        "raw_bytes": {
          "bytes": 20780,
          "sha256": "406363ba4db6c6ca8d71f406abce0efe039a951f1bc7b538587d5223e411a0cf"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "52",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:c6c317e4316ff82bf1e187209d9f5b8474c84243362865cd2a08f9476268e390",
        "revision": 1,
        "sha256": "77b3af19e3502b0b5afc8c30358547a659a0aa3aa1cb527ce405a40db30b0301"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "ebd626df135ab15d7b4b814de9e8358442f5cc05da0f16fe941f119adaef9029"
      },
      "manuscript_sha256": "92dc32ca182606097ac0347b9382b195992ec17389c680f68eafcbb07ac4d85f",
      "guide_sha256": "cb6bb87e70913f6f54923f8a4e071cb1e0de43246e630e2aa8c48a52e5c42004",
      "url": "../../cards/c6c317e4316ff82bf1e187209d9f5b8474c84243362865cd2a08f9476268e390/versions/gss-r1-ebd626df135ab15d/index.html",
      "card_json": "../../cards/c6c317e4316ff82bf1e187209d9f5b8474c84243362865cd2a08f9476268e390/versions/gss-r1-ebd626df135ab15d/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SubhomogeneousCharacterization.lean.html?from=52&start=47&end=55#L47",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SubhomogeneousCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SubhomogeneousCharacterization.lean",
        "raw_bytes": {
          "bytes": 4955,
          "sha256": "29c46e11f9b1103a7e357be67836c25c10fa0851263b151de31fd431c36b1458"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "50",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:06c5414a063d30311a7d885a6b5c3514d607fe9424d4f9d437cc9cfb38f1f597",
        "revision": 1,
        "sha256": "297a88ec2fbf93cca71b48d92709bbff9146edcb29d3ff60a2bb7a85a84c4ca5"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "3e5ca9e1f3eb6c3c03253ca13353777f0abc3d9d52ded96e6e09e6a14a379fac"
      },
      "manuscript_sha256": "c0e21056591e27d0bb0a4530f9f103625df2f44d23a96615eed388f6cf1be0f0",
      "guide_sha256": "32939be18d3cbc01f6a40049cf59077d1ddde2147242d5fc87d9e043b5a303e1",
      "url": "../../cards/06c5414a063d30311a7d885a6b5c3514d607fe9424d4f9d437cc9cfb38f1f597/versions/gss-r1-3e5ca9e1f3eb6c3c/index.html",
      "card_json": "../../cards/06c5414a063d30311a7d885a6b5c3514d607fe9424d4f9d437cc9cfb38f1f597/versions/gss-r1-3e5ca9e1f3eb6c3c/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean.html?from=50&start=311&end=325#L311",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/GCRCharacterization.lean",
        "raw_bytes": {
          "bytes": 16255,
          "sha256": "99db060f568a62d68d8f656cbe0ba8fe965f35f348b2c5755c8c503398a9fe12"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "26",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:40149bd49114dfa869eef625e06a0138beb53d7b8946c51f162e0e196f171ac1",
        "revision": 1,
        "sha256": "ce590b80d388112ae6332e0b202a01bd73f95ad1fc373f5baa7b52e1c25eb7c3"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "ca68b7db0ee7c38c2076bbd4fb01b99ff35f83a1fd2131539342b90cc90c8dc0"
      },
      "manuscript_sha256": "ab97afd84ced4d0c354a06fe0e9f8cca134c88b825687f17769f16c07de45834",
      "guide_sha256": "2455b9c609222f4c187454b927837fe0f13f5b7dd859f055c2b7b3d090d6ff4e",
      "url": "../../cards/40149bd49114dfa869eef625e06a0138beb53d7b8946c51f162e0e196f171ac1/versions/gss-r1-ca68b7db0ee7c38c/index.html",
      "card_json": "../../cards/40149bd49114dfa869eef625e06a0138beb53d7b8946c51f162e0e196f171ac1/versions/gss-r1-ca68b7db0ee7c38c/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralPreserver.lean.html?from=26&start=33&end=37#L33",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralPreserver.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/SpectralPreserver.lean",
        "raw_bytes": {
          "bytes": 4220,
          "sha256": "782bbe283cd76b8dcfe735c63264a608686e3a2cac55b9851c3a88fd2634e624"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "61",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
      "level": 8,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:512cd884f8448768e9babb08ddd780e0eb15cf34727aa9a1c4925695669752ef",
        "revision": 1,
        "sha256": "d3819b8587cdd7a5ab6e237e096babd8b775b50e5aff04bd2aad2bab7c336203"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "06ab3118631304ff7906e067cdb106f1a6a180bc37e18fc9ddd9096bc0b95153"
      },
      "manuscript_sha256": "32d001c1843e130f65d88ff60d63537cfad111d91357e561a82f40a80e73797b",
      "guide_sha256": "ba22fa5401d6fae837e182fd298e58ea75da0e3da8e3fc5d16cb467e0be38a5d",
      "url": "../../cards/512cd884f8448768e9babb08ddd780e0eb15cf34727aa9a1c4925695669752ef/versions/gss-r1-06ab3118631304ff/index.html",
      "card_json": "../../cards/512cd884f8448768e9babb08ddd780e0eb15cf34727aa9a1c4925695669752ef/versions/gss-r1-06ab3118631304ff/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/BoundedOperatorModelCharacterization.lean.html?from=61&start=273&end=302#L273",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/BoundedOperatorModelCharacterization.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/BoundedOperatorModelCharacterization.lean",
        "raw_bytes": {
          "bytes": 14478,
          "sha256": "4eae9121e1d7550620f7084c8bf2997868d77017b83a9031e8c1fef9e6c2f044"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "59",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
      "level": 9,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:6b0c4cdd1964f6eb8c8b457a0b1b9b14bf8af4b70b47d74a6675a0a58e03bac5",
        "revision": 1,
        "sha256": "1927a6ba1973a8fbf9e34ac0b7734e6d376188517efec7b2c08937058af786ea"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "94476287b229a2fae4be8742f8a01233a31d78e32be41d097680a57cbf219ede"
      },
      "manuscript_sha256": "b5c8300d8eb0a88682faf869992f55867bdedc627c9ae256531e9fa6059f1738",
      "guide_sha256": "2254b1d2d31009b25a5dd2d20c1452b7866f353fcfae4f1280899edb0a64f3f3",
      "url": "../../cards/6b0c4cdd1964f6eb8c8b457a0b1b9b14bf8af4b70b47d74a6675a0a58e03bac5/versions/gss-r1-94476287b229a2fa/index.html",
      "card_json": "../../cards/6b0c4cdd1964f6eb8c8b457a0b1b9b14bf8af4b70b47d74a6675a0a58e03bac5/versions/gss-r1-94476287b229a2fa/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryFiniteDimensionalRigidity.lean.html?from=59&start=88&end=126#L88",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryFiniteDimensionalRigidity.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryFiniteDimensionalRigidity.lean",
        "raw_bytes": {
          "bytes": 8690,
          "sha256": "073523a9afa33efe3ab58ab6fdf1e4c919a954bf5f174e985374ff934c25f53c"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "58",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
      "level": 9,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:246001db089358ca2048f2fa1f24011fbdceaba5e6ebb2ec6b7e18c4900cf1c0",
        "revision": 1,
        "sha256": "3be45b0c975f153e673a3bef4565d4102f60f506187c006d685dd5c724c425bc"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "e860795177df166d057812a1c02c1c9ed14eba453dfd7bd4798a404bcff12963"
      },
      "manuscript_sha256": "6dd11a0259518e5cc1181fd46265c04627c1db11cf272b2c7fb557e0916ff848",
      "guide_sha256": "9403fc0250f6daa61f4de9a9b5b5b2669c2d6e31d7dad94c9264cbe1517fa582",
      "url": "../../cards/246001db089358ca2048f2fa1f24011fbdceaba5e6ebb2ec6b7e18c4900cf1c0/versions/gss-r1-e860795177df166d/index.html",
      "card_json": "../../cards/246001db089358ca2048f2fa1f24011fbdceaba5e6ebb2ec6b7e18c4900cf1c0/versions/gss-r1-e860795177df166d/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/CompactRepresentationRigidity.lean.html?from=58&start=114&end=153#L114",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/CompactRepresentationRigidity.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/CompactRepresentationRigidity.lean",
        "raw_bytes": {
          "bytes": 8336,
          "sha256": "94c92a49a55ce7989ac42cf271285f2c630c6ea1a74983ea2771a22723e13924"
        },
        "release_scope": "v0.5.0"
      }
    },
    {
      "node_id": "60",
      "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
      "level": 9,
      "card_ref": {
        "record_type": "LFH_DECLARATION_CARD",
        "uid": "lfh:lfh-declaration-card:sha256:8b8480a55df0a4e96204c8b9b774c40d1fb0bdee6a15822103f93c366da3f62c",
        "revision": 1,
        "sha256": "dde125463da1e031393af76e061bec98f86ed03490b2aed8cd2156da705982e3"
      },
      "exposition_ref": {
        "revision": 1,
        "sha256": "d8658c3bcbb13dd0cb1d790ceefd6164e5529339b826ee92ddc120d340481184"
      },
      "manuscript_sha256": "c8a82d70f3fa5e9841f68a5908f75ec9112222026fa71c70eabd222f14edf351",
      "guide_sha256": "868ca3d13066e39e31a69e48023f70dcee21ac4cf9a5135d04a47247db869d5a",
      "url": "../../cards/8b8480a55df0a4e96204c8b9b774c40d1fb0bdee6a15822103f93c366da3f62c/versions/gss-r1-d8658c3bcbb13dd0/index.html",
      "card_json": "../../cards/8b8480a55df0a4e96204c8b9b774c40d1fb0bdee6a15822103f93c366da3f62c/versions/gss-r1-d8658c3bcbb13dd0/card.json",
      "source_binding": {
        "source_view": "../../sources/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryFiniteDimensionalRigidity.lean.html?from=60&start=147&end=165#L147",
        "fixed_original": "https://github.com/r-tanaka-math/mathlib-annex/blob/ac405356bb98afed954da9b9c795d23cc8d5d149/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryFiniteDimensionalRigidity.lean",
        "raw": "../../raw/gss-v0.5.0/MathlibAnnex/Analysis/CStarAlgebra/GeometricStructure/ElementaryFiniteDimensionalRigidity.lean",
        "raw_bytes": {
          "bytes": 8690,
          "sha256": "073523a9afa33efe3ab58ab6fdf1e4c919a954bf5f174e985374ff934c25f53c"
        },
        "release_scope": "v0.5.0"
      }
    }
  ],
  "node_count": 69,
  "source_binding": {
    "gss_release": "v0.5.0",
    "gss_commit": "ac405356bb98afed954da9b9c795d23cc8d5d149",
    "legacy_reused_model_release": "v0.4.0",
    "legacy_source_unchanged": true,
    "qualification": "CHECKPOINT_ASSISTED",
    "independent_clean_single_runner": "NOT_RUN"
  },
  "graph": {
    "node_count": 69,
    "display_edge_count": 205,
    "reachability_count": 829,
    "maximum_level": 9,
    "orientation": "dependency -> consumer; type AND value; omitted helpers traversed",
    "full_formal_graph_sha256": "215b1a4afecc5daf3e92150b6fd797f86f0806d84c6b91aa5cd3c6f02014a092",
    "nodes": [
      {
        "selection_key": "1",
        "declaration": "ClosureSpace",
        "level": 0
      },
      {
        "selection_key": "38",
        "declaration": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "level": 0
      },
      {
        "selection_key": "c0-direct-sum",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "level": 0
      },
      {
        "selection_key": "irreducible-spectrum",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "level": 0
      },
      {
        "selection_key": "is-compact-operator-model",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "level": 0
      },
      {
        "selection_key": "primitive-spectrum",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "level": 0
      },
      {
        "selection_key": "15",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "level": 0
      },
      {
        "selection_key": "3",
        "declaration": "NormedSpace.supportKernelUnion",
        "level": 0
      },
      {
        "selection_key": "35",
        "declaration": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "level": 0
      },
      {
        "selection_key": "12",
        "declaration": "ClosureSpace.FiniteHomeomorph",
        "level": 1
      },
      {
        "selection_key": "2",
        "declaration": "ClosureSpace.HullKernel.space",
        "level": 1
      },
      {
        "selection_key": "7",
        "declaration": "ClosureSpace.Linked",
        "level": 1
      },
      {
        "selection_key": "ideal-c0-sum-equivalence",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "level": 1
      },
      {
        "selection_key": "compact-operator-c0-sum",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "level": 1
      },
      {
        "selection_key": "compact-model-space",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "level": 1
      },
      {
        "selection_key": "14",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "level": 1
      },
      {
        "selection_key": "4",
        "declaration": "NormedSpace.GeometricStructureSpace",
        "level": 1
      },
      {
        "selection_key": "13",
        "declaration": "ClosureSpace.IsLinkedSet",
        "level": 2
      },
      {
        "selection_key": "8",
        "declaration": "ClosureSpace.component",
        "level": 2
      },
      {
        "selection_key": "compact-c0-sum-equivalence",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "level": 2
      },
      {
        "selection_key": "16",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "level": 2
      },
      {
        "selection_key": "27",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "level": 2
      },
      {
        "selection_key": "5",
        "declaration": "NormedSpace.geometricStructureClosure",
        "level": 2
      },
      {
        "selection_key": "47",
        "declaration": "ClosureSpace.HasCompactOperatorHomeomorph",
        "level": 3
      },
      {
        "selection_key": "46",
        "declaration": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "level": 3
      },
      {
        "selection_key": "44",
        "declaration": "ClosureSpace.HasContinuousFiniteConjugation",
        "level": 3
      },
      {
        "selection_key": "48",
        "declaration": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "level": 3
      },
      {
        "selection_key": "57",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "level": 3
      },
      {
        "selection_key": "19",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "level": 3
      },
      {
        "selection_key": "18",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "level": 3
      },
      {
        "selection_key": "32",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "level": 3
      },
      {
        "selection_key": "31",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "level": 3
      },
      {
        "selection_key": "17",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate",
        "level": 3
      },
      {
        "selection_key": "33",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "level": 3
      },
      {
        "selection_key": "29",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "level": 3
      },
      {
        "selection_key": "30",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "level": 3
      },
      {
        "selection_key": "9",
        "declaration": "NormedSpace.GeometricSpectrum",
        "level": 3
      },
      {
        "selection_key": "10",
        "declaration": "NormedSpace.PrimitiveGeometricSpectrum",
        "level": 3
      },
      {
        "selection_key": "6",
        "declaration": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "level": 3
      },
      {
        "selection_key": "55",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "level": 4
      },
      {
        "selection_key": "25",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "level": 4
      },
      {
        "selection_key": "56",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "level": 4
      },
      {
        "selection_key": "28",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "level": 4
      },
      {
        "selection_key": "20",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "level": 4
      },
      {
        "selection_key": "36",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "level": 4
      },
      {
        "selection_key": "34",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "level": 4
      },
      {
        "selection_key": "37",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "level": 4
      },
      {
        "selection_key": "11",
        "declaration": "NormedSpace.geometricSpectrumToPrimitive",
        "level": 4
      },
      {
        "selection_key": "53",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "level": 5
      },
      {
        "selection_key": "21",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "level": 5
      },
      {
        "selection_key": "42",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "level": 5
      },
      {
        "selection_key": "40",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "level": 5
      },
      {
        "selection_key": "39",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "level": 5
      },
      {
        "selection_key": "41",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "level": 6
      },
      {
        "selection_key": "22",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "level": 6
      },
      {
        "selection_key": "24",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "level": 7
      },
      {
        "selection_key": "23",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "level": 7
      },
      {
        "selection_key": "54",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "level": 8
      },
      {
        "selection_key": "43",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "level": 8
      },
      {
        "selection_key": "45",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "level": 8
      },
      {
        "selection_key": "49",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "level": 8
      },
      {
        "selection_key": "51",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "level": 8
      },
      {
        "selection_key": "52",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "level": 8
      },
      {
        "selection_key": "50",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "level": 8
      },
      {
        "selection_key": "26",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "level": 8
      },
      {
        "selection_key": "61",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "level": 8
      },
      {
        "selection_key": "59",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "level": 9
      },
      {
        "selection_key": "58",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "level": 9
      },
      {
        "selection_key": "60",
        "declaration": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "level": 9
      }
    ],
    "edges": [
      [
        "ClosureSpace",
        "ClosureSpace.FiniteHomeomorph"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.HullKernel.space"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.Linked"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "ClosureSpace.HasContinuousFiniteConjugation"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace.HasContinuousFiniteCompactComparison",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace.HasContinuousFiniteConjugation",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.geometricStructureClosure"
      ],
      [
        "ClosureSpace.IsLinkedSet",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "ClosureSpace.Linked",
        "ClosureSpace.IsLinkedSet"
      ],
      [
        "ClosureSpace.Linked",
        "ClosureSpace.component"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "ClosureSpace.component",
        "ClosureSpace.HasContinuousFiniteConjugation"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "ClosureSpace.component",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "ClosureSpace.component",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "NormedSpace.geometricStructureClosure"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "ClosureSpace.HasCompactOperatorHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.GeometricStructureSpace"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ]
    ],
    "pairs": [
      [
        "ClosureSpace",
        "ClosureSpace.FiniteHomeomorph"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.HasCompactOperatorHomeomorph"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.HasContinuousFiniteConjugation"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.HullKernel.space"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.IsLinkedSet"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.Linked"
      ],
      [
        "ClosureSpace",
        "ClosureSpace.component"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "ClosureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "ClosureSpace",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "ClosureSpace",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "ClosureSpace",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "ClosureSpace",
        "NormedSpace.geometricStructureClosure"
      ],
      [
        "ClosureSpace",
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "ClosureSpace.HasContinuousFiniteConjugation"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "ClosureSpace.FiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.HasCompactOperatorHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace.HasContinuousFiniteCompactComparison",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace.HasContinuousFiniteConjugation",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "ClosureSpace.HasCompactOperatorHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.geometricStructureClosure"
      ],
      [
        "ClosureSpace.HullKernel.space",
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
      ],
      [
        "ClosureSpace.IsLinkedSet",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "ClosureSpace.Linked",
        "ClosureSpace.HasContinuousFiniteConjugation"
      ],
      [
        "ClosureSpace.Linked",
        "ClosureSpace.IsLinkedSet"
      ],
      [
        "ClosureSpace.Linked",
        "ClosureSpace.component"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "ClosureSpace.Linked",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "ClosureSpace.Linked",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "ClosureSpace.Linked",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "ClosureSpace.Linked",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "ClosureSpace.component",
        "ClosureSpace.HasContinuousFiniteConjugation"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "ClosureSpace.component",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "ClosureSpace.component",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "ClosureSpace.component",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "ClosureSpace.component",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "NormedSpace.GeometricSpectrum",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "ClosureSpace.HasCompactOperatorHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "NormedSpace.geometricStructureClosure"
      ],
      [
        "NormedSpace.GeometricStructureSpace",
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "NormedSpace.PrimitiveGeometricSpectrum",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "NormedSpace.geometricSpectrumToPrimitive",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "ClosureSpace.HasCompactOperatorHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.geometricStructureClosure",
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "ClosureSpace.HasCompactOperatorHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "ClosureSpace.HasContinuousFiniteCompactComparison"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.GeometricSpectrum"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.GeometricStructureSpace"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.PrimitiveGeometricSpectrum"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.geometricSpectrumToPrimitive"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.geometricStructureClosure"
      ],
      [
        "NormedSpace.supportKernelUnion",
        "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
      ],
      [
        "Projectivization.exists_semilinearEquiv_of_finite_span",
        "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
      ]
    ],
    "witness_paths": [
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.HullKernel.space",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HullKernel.space"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "NormedSpace.GeometricStructureSpace",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "NormedSpace.geometricStructureClosure",
        "path": [
          "ClosureSpace",
          "NormedSpace.geometricStructureClosure"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "NormedSpace.geometricStructureClosure",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "NormedSpace.geometricStructureClosure",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.geometricStructureClosure"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "NormedSpace.geometricStructureClosure",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.geometricStructureClosure"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "path": [
          "ClosureSpace.HullKernel.space",
          "ClosureSpace.HullKernel.homeomorphOfMemIff",
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.Linked",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Linked"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.component",
        "path": [
          "ClosureSpace",
          "ClosureSpace.component"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "ClosureSpace.component",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "ClosureSpace",
          "ClosureSpace.componentFamily",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.componentFamily",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "NormedSpace.GeometricSpectrum",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "ClosureSpace.componentFamily",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "NormedSpace.PrimitiveGeometricSpectrum",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.primitiveGeometricSpectrumFamily",
          "NormedSpace.PrimitiveGeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "NormedSpace.PrimitiveGeometricSpectrum",
        "path": [
          "ClosureSpace.HullKernel.space",
          "ClosureSpace.HullKernel.componentKernel",
          "ClosureSpace.HullKernel.componentKernelFamily",
          "NormedSpace.primitiveGeometricSpectrumFamily",
          "NormedSpace.PrimitiveGeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "NormedSpace.PrimitiveGeometricSpectrum",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.HullKernel.componentKernel",
          "ClosureSpace.HullKernel.componentKernelFamily",
          "NormedSpace.primitiveGeometricSpectrumFamily",
          "NormedSpace.PrimitiveGeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "NormedSpace.PrimitiveGeometricSpectrum",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HullKernel.space",
          "ClosureSpace.HullKernel.componentKernel",
          "ClosureSpace.HullKernel.componentKernelFamily",
          "NormedSpace.primitiveGeometricSpectrumFamily",
          "NormedSpace.PrimitiveGeometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "NormedSpace.PrimitiveGeometricSpectrum",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "ClosureSpace.HullKernel.componentKernel",
          "ClosureSpace.HullKernel.componentKernelFamily",
          "NormedSpace.primitiveGeometricSpectrumFamily",
          "NormedSpace.PrimitiveGeometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "ClosureSpace.HullKernel.space",
          "ClosureSpace.HullKernel.componentPointToComponentKernelPoint",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.GeometricSpectrum",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "ClosureSpace",
          "ClosureSpace.ComponentPoint",
          "ClosureSpace.HullKernel.componentPointToComponentKernelPoint",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.HullKernel.componentPointToComponentKernelPoint._proof_1",
          "ClosureSpace.HullKernel.componentPointToComponentKernelPoint",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "NormedSpace.geometricSpectrumToPrimitive",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "ClosureSpace.HullKernel.componentPointToComponentKernelPoint._proof_1",
          "ClosureSpace.HullKernel.componentPointToComponentKernelPoint",
          "NormedSpace.geometricSpectrumToPrimitive"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.FiniteHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.FiniteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.IsLinkedSet",
        "path": [
          "ClosureSpace",
          "ClosureSpace.IsLinkedSet"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "ClosureSpace.IsLinkedSet",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.IsLinkedSet"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "path": [
          "NormedSpace.supportKernelUnion",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_setOf_exists_pureState_unitaryTranslate"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "ClosureSpace.Linked",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_related_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_related_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_related_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_related_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "ClosureSpace.Linked",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_related_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.related_extremeKernel_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.related_extremeKernel_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.related_extremeKernel_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.componentFamily",
          "NormedSpace.geometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_toGeometricSpectrum_extremeKernel_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.related_extremeKernel_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_toGeometricSpectrum_extremeKernel_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_kernel_mem_geometricSpectrum"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "ClosureSpace",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "NormedSpace.geometricSpectrumToPrimitive",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumToPrimitive",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "ClosureSpace",
          "ClosureSpace.ComponentPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.geometricSpectrumToPrimitive",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_toGeometricSpectrum_extremeKernel_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_toGeometricSpectrum_extremeKernel_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph.toTopologicalHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.HullKernel.componentKernel",
          "ClosureSpace.HullKernel.componentKernelFamily",
          "NormedSpace.primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_toGeometricSpectrum_extremeKernel_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.extremeKernel_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_toGeometricSpectrum_extremeKernel_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph.toTopologicalHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.componentFamily",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructurePreimageHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "NormedSpace.geometricSpectrumKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamily_geometricStructureFamily_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullEquiv._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructurePreimageHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamily_geometricStructureFamily_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullEquiv._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructurePreimageHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamily_geometricStructureFamily_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullEquiv._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.preimageFamilyKernelHullHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructurePreimageHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.componentFamily",
          "NormedSpace.geometricSpectrumFamily",
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.GPoint",
          "NormedSpace.geometricSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.image_component",
          "ClosureSpace.Homeomorph.image_componentClosure",
          "ClosureSpace.Homeomorph.pMap_toPPoint",
          "ClosureSpace.Homeomorph.continuous_pMap",
          "ClosureSpace.Homeomorph.continuous_gMap",
          "ClosureSpace.Homeomorph.gHomeomorph",
          "NormedSpace.geometricSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_pureStateKernel_eq_matrixCoefficientKernelFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "ClosureSpace",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "ClosureSpace.Linked",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_related_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.finitelyContinuous_normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.finitelyContinuous_normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.finitelyContinuous_normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.finitelyContinuous_normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartSemilinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartSemilinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartSemilinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartSemilinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearMap",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "ClosureSpace.Linked",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "ClosureSpace",
          "ClosureSpace.IsClosed",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.isClosed_pair_normalPartPoint_of_span_ne",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq"
        ]
      },
      {
        "dependency": "ClosureSpace.IsLinkedSet",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "ClosureSpace.IsLinkedSet",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "ClosureSpace",
          "ClosureSpace.IsLinkedSet",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.IsLinkedSet",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.isLinkedSet_normalPartSourceFiber",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.isLinkedSet_normalPartSourceFiber",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.isLinkedSet_normalPartSourceFiber",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.isLinkedSet_normalPartSourceFiber",
          "MathlibAnnex.Analysis.CStarAlgebra.maximal_isLinkedSet_normalPart_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.FiniteHomeomorph.exists_prod_equivalences_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "ClosureSpace",
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.FiniteHomeomorph.exists_prod_equivalences_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv_eq_refl_or_star",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.not_finiteDimensional_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv_eq_refl_or_star",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.FiniteHomeomorph.exists_prod_equivalences_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.not_finiteDimensional_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.FiniteHomeomorph.exists_prod_equivalences_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.not_finiteDimensional_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.aleph0_le_rank_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.three_le_rank_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.FiniteHomeomorph.exists_prod_equivalences_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_classification_eq"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous_of_not_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_continuousLinearEquiv_or_conj_eq_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous_of_not_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.FiniteHomeomorph.exists_prod_equivalences_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.setOf_inner_apply_eq_zero_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.restrictedMatrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartPoint",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationMap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "ClosureSpace",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.geometricSpectrumKernel_toGeometricSpectrum_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.component_matrixCoefficientKernel_eq_univ_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_faithful_representation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_faithful_representation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isClosed_component_matrixCoefficientKernel_iff_normalPart_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.component_matrixCoefficientKernel_eq_univ_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_faithful_representation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_faithful_representation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_representation"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.HasContinuousFiniteConjugation",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasContinuousFiniteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "ClosureSpace.HasContinuousFiniteConjugation",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.HasContinuousFiniteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "ClosureSpace.HasContinuousFiniteConjugation",
        "path": [
          "ClosureSpace.component",
          "ClosureSpace.HasContinuousFiniteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "ClosureSpace.HasContinuousFiniteConjugation",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "ClosureSpace.HasContinuousFiniteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.HasContinuousFiniteConjugation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "ClosureSpace.HasContinuousFiniteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasContinuousFiniteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.HasContinuousFiniteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.singletonImageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.singletonImageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.adjointSandwich_image_eq_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.unitary_mul_image_eq_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_unitary_invariant_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_operatorIdeal_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_compactOperatorModel_of_singleton_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.singletonImageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.adjointSandwich_image_eq_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.unitary_mul_image_eq_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_unitary_invariant_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_operatorIdeal_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_compactOperatorModel_of_singleton_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.singletonImageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_faithful_pureState",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_singleton_normalPart_finiteConjugation_model",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_unitary_invariant_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_operatorIdeal_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_compactOperatorModel_of_singleton_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartLinearFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.adjointSandwich_image_eq_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.unitary_mul_image_eq_of_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_unitary_invariant_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_image_operatorIdeal_of_singleton",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_compactOperatorModel_of_singleton_finiteConjugation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_iff_exists_component_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_compact_conjugate_homeomorph_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasImageNormalPartFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_compact_operators_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_hasContinuousFiniteConjugation_of_isCompactOperatorModel_all_dimensions",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_compactOperatorModel_iff_singleton_finiteConjugation"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasContinuousFiniteCompactComparison"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.HasContinuousFiniteCompactComparison"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "ClosureSpace.HasContinuousFiniteCompactComparison"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "ClosureSpace.HasContinuousFiniteCompactComparison"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "ClosureSpace.HasContinuousFiniteCompactComparison"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "ClosureSpace.HasContinuousFiniteCompactComparison"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.HasCompactOperatorHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasCompactOperatorHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "ClosureSpace.HasCompactOperatorHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "ClosureSpace.HasCompactOperatorHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "ClosureSpace.HasCompactOperatorHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "ClosureSpace.HasCompactOperatorHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "ClosureSpace.HasCompactOperatorHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "ClosureSpace.HasCompactOperatorHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "ClosureSpace.HasCompactOperatorHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "ClosureSpace.HasCompactOperatorHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HasContinuousFiniteCompactComparison",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "ClosureSpace.HasContinuousFiniteCompactComparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasContinuousFiniteCompactComparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.HasContinuousFiniteCompactComparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartLinearFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_isCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.compact_le_range_of_component_compact_comparisons",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_compact_le_iff_component_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_compact_le_iff_component_compact_comparison"
        ]
      },
      {
        "dependency": "ClosureSpace.HasCompactOperatorHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.HasCompactOperatorHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasCompactOperatorHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.toEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_isCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_homeomorph_compact_of_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_range_eq_compact_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.HasFiniteDimensionalCompactComparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_isCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_eq_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.HasFiniteDimensionalCompactHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.HasFiniteDimensionalCompactComparison",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_isCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFiniteHomeomorphSwap",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_projective_swapped_factors_preserve_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_component_homeomorph_eq_of_finiteDimensional_compact_comparison",
          "MathlibAnnex.Analysis.CStarAlgebra.component_hasFiniteDimensionalCompactComparison_iff_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finiteDimensional_finrank_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_irreducible_finrank_le_iff_component_compact_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.image_component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithfulImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.toEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartStarHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithfulImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_isCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_iff_of_geometricStructure_homeomorph"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "ClosureSpace",
          "ClosureSpace.toTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "ClosureSpace.HullKernel.space",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.isCompactlyRepresented_representationOfEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.isCompactlyRepresented_representationOfEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "ClosureSpace.Linked",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_linked_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compact_of_forall_pureStateRepresentative_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.forall_pureStateRepresentative_range_eq_compact_iff_forall_irreducible_range_eq_compact",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_isCompactlyRepresented_iff"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum.nonUnitalCStarAlgebra",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "ClosureSpace",
          "ClosureSpace.toTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "ClosureSpace.HullKernel.space",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_eq_compactOperatorStarSubalgebra_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.range_gnsRepresentation_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "ClosureSpace.Linked",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.unitaryEquivalent_of_linked_matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_norm_eq_one_apply_eq_one_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_unitBallSupportFace_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_unitaryEquivalent_gnsRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.exists_pureState_kernelIdeal_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.ofRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.kernelIntersection_univ_eq_bot",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_injective",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isometry_reducedAtomicRepresentation",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.reducedAtomicRepresentation_spec_of_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureHomeomorphOfStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.HasCompactOperatorHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "ClosureSpace.HasCompactOperatorHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.toEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasCompactOperatorHomeomorph_component_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasCompactOperatorHomeomorph_component_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isTopologizable_primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.hilbertBasis_lift_mk_eq_of_matched_coordinate",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.nonempty_linearIsometryEquiv_of_matched_coordinate",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.fiberLinearIsometryEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityFiberEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isTopologizable_primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_isCompactlyRepresented"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureHomeomorphOfStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.HasCompactOperatorHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "ClosureSpace.HasCompactOperatorHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.toEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasCompactOperatorHomeomorph_component_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasCompactOperatorHomeomorph_component_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isTopologizable_primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.hilbertBasis_lift_mk_eq_of_matched_coordinate",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.nonempty_linearIsometryEquiv_of_matched_coordinate",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.fiberLinearIsometryEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityFiberEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isTopologizable_primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_compactOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_compactOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureHomeomorphOfStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.compactC0Decomposition",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "ClosureSpace.HasCompactOperatorHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "ClosureSpace.HasCompactOperatorHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.toEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.image_normalPart_eq_component",
          "MathlibAnnex.Analysis.CStarAlgebra.imageNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasCompactOperatorHomeomorph_component_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_representation_normalPart_homeomorph_component",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_iff_component_compact_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hasCompactOperatorHomeomorph_component_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isTopologizable_primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.hilbertBasis_lift_mk_eq_of_matched_coordinate",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.nonempty_linearIsometryEquiv_of_matched_coordinate",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.fiberLinearIsometryEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityFiberEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_compactOperatorStarSubalgebra_of_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.forall_pure_state_range_eq_compact_of_component_compact_homeomorphs",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.range_pureStateRepresentative_eq_compact_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.isTopologizable_primitiveGeometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.discreteTopology_primitiveSpectrum_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum.isCompactlyRepresented_reducedAtomicRepresentation_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorphOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum.indexEquivOfGeometricStructure",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityIndexEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.compactDirectSumRigidityStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph_of_nonempty",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_compact_direct_sum_models_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_isCompactlyRepresented_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isCompactlyRepresented",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_finiteDimensional_or"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricStructureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureClosure",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "ClosureSpace",
          "ClosureSpace.Homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.HullKernel.space",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "ClosureSpace.HullKernel.space",
          "NormedSpace.geometricStructureClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.supportKernelUnion",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.supportKernelUnion",
          "NormedSpace.geometricStructureFamily",
          "NormedSpace.GeometricStructureSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.geometricStructureHomeomorphOfBirkhoffJames",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureHomeomorphOfStarAlgEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.component",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.FiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "ClosureSpace.FiniteHomeomorph",
          "ClosureSpace.FiniteHomeomorph.toEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectivizationEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_iff_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.component_matrixCoefficientKernel_eq_family",
          "MathlibAnnex.Analysis.CStarAlgebra.component_restrictedMatrixCoefficientKernel_eq_normalPart",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.GeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.GeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.imageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.coefficientImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithfulImageGeometricStructureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_evaluation",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_scalar_types",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "Projectivization.exists_semilinearEquiv_of_finite_span",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "Projectivization.exists_semilinearEquiv_of_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_first_semilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstScalarEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.finite_and_finrank_eq_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.not_finiteDimensional_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.aleph0_le_rank_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.three_le_rank_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "ClosureSpace.Linked",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "ClosureSpace.Linked",
          "ClosureSpace.componentSetoid",
          "ClosureSpace.Related",
          "ClosureSpace.component",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.exists_pureState_unitaryTranslate_of_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.isPureNonUnitalState_extremeAbsoluteState",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_surjective",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_pureState_image_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_normalPart_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_normalPart_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_and_inverse_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_and_inverse_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartLinearMap_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPart_equiv_iff_of_linear_point_eq_or_swap",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_same_type_normalPart_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.isMaximalFace_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricStructureFamily_eq_image_ker_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.mem_geometricStructureFamily_iff_exists_mem_extremePoints_dual_closedBall",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.ker_matrixCoefficient_mem_geometricStructureFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.matrixCoefficientKernel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_normalPart_transport",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "LinearEquiv.regularity_of_isClosed_image_hyperplane",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "LinearEquiv.regularity_of_isClosed_image_hyperplane",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartFirstSemilinearEquiv_symm_regularity",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartFirstSemilinearEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_semilinear_factors_continuous",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_inclusion",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_selected_operator_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartPoint_iff_span_eq_or_span_eq",
          "MathlibAnnex.Analysis.CStarAlgebra.linked_normalPartProjectivizationEquiv_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_or_swapped",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_normalPart_projective_factors_preserving_finite_span",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartProjectiveFirstFactor",
          "MathlibAnnex.Analysis.CStarAlgebra.finite_iff_of_normalPart_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.eq_top_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartSemilinearFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPartLinearFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.continuous_normalPartToCompactFiniteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_of_isCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_forall_eq_irreducibleSpectrum_compact_operators",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.PrimitiveSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.instTopologicalSpace",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.PrimitiveGeometricSpectrum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.PrimitiveGeometricSpectrum",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "NormedSpace.geometricSpectrumToPrimitive",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "NormedSpace.geometricSpectrumToPrimitive",
          "NormedSpace.geometricSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumTopology",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.related_matrixCoefficientKernel_iff_unitaryEquivalent",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.toGeometricSpectrum_eq_iff",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.toGeometricSpectrum_bijective",
          "MathlibAnnex.Analysis.CStarAlgebra.IrreducibleSpectrum.equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveKernelFamily_eq_primitiveGeometricSpectrumFamily",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric._proof_1",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumToPrimitive_toGeometricSpectrum_pureStateKernel_val",
          "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalPureState.geometricSpectrumToPrimitive_toGeometricSpectrum_val",
          "MathlibAnnex.Analysis.CStarAlgebra.primitiveSpectrumEquivGeometric_kernel",
          "MathlibAnnex.Analysis.CStarAlgebra.geometricSpectrumKernel_equivGeometricSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.image_irreducibleSpectrumClosure",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumClosureHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.irreducibleSpectrumHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.faithful_and_normalPart_eq_univ_of_singleton_irreducibleSpectrum",
          "MathlibAnnex.Analysis.CStarAlgebra.normalPart_compactOperatorStarSubalgebra_eq_univ",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph._proof_18",
          "MathlibAnnex.Analysis.CStarAlgebra.compactNormalPartHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_of_continuous_finiteHomeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.compactOperatorStarSubalgebra_le_iff_of_normalPart_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.hilbertBasis_lift_mk_eq_of_geometricStructure_homeomorph_of_compact_le",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_hilbertBasis_index_equiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_linearIsometryEquiv_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.exists_faithful_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_of_boundedOperatorModel_of_geometricStructure_homeomorph",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_isBoundedOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_boundedOperatorEquiv",
          "MathlibAnnex.Analysis.CStarAlgebra.nonempty_starAlgEquiv_iff_nonempty_geometricStructure_homeomorph_of_exists_boundedOperatorEquiv"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.compactC0SumEquivOfDense"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.compactModelSubspace",
          "MathlibAnnex.Analysis.CStarAlgebra.MinimalClosedStarIdeal.CompactModelSpace"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.CompactOperatorC0Sum"
        ]
      },
      {
        "dependency": "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
        "consumer": "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense",
        "path": [
          "MathlibAnnex.Analysis.CStarAlgebra.C0DirectSum",
          "MathlibAnnex.Analysis.CStarAlgebra.ClosedStarIdeal.c0SumEquivOfDense"
        ]
      }
    ],
    "focus_semantics": "target plus predecessor dependency closure; Used by excluded"
  },
  "route_presets": [
    {
      "id": "g1",
      "label": "Closure spaces and norm geometry",
      "status": "ACTIVE",
      "activation_allowed": true,
      "terminal_node_ids": [
        "1",
        "2",
        "3",
        "4",
        "5",
        "6",
        "7",
        "8",
        "9",
        "10",
        "11",
        "12",
        "13"
      ],
      "expected_visible_ids": [
        "1",
        "10",
        "11",
        "12",
        "13",
        "2",
        "3",
        "4",
        "5",
        "6",
        "7",
        "8",
        "9"
      ],
      "expected_visible_count": 13,
      "bridge": "Begin with hull–kernel closure on the kernel families obtained from faces. Closure need not be topological; finite continuity tests finite subsets, whereas continuity tests every subset."
    },
    {
      "id": "g2",
      "label": "Faces, pure states and spectra",
      "status": "ACTIVE",
      "activation_allowed": true,
      "terminal_node_ids": [
        "14",
        "15",
        "16",
        "17",
        "18",
        "19",
        "20",
        "21",
        "22",
        "23",
        "24",
        "25",
        "26",
        "irreducible-spectrum",
        "primitive-spectrum"
      ],
      "expected_visible_ids": [
        "1",
        "10",
        "11",
        "12",
        "14",
        "15",
        "16",
        "17",
        "18",
        "19",
        "2",
        "20",
        "21",
        "22",
        "23",
        "24",
        "25",
        "26",
        "3",
        "4",
        "5",
        "7",
        "8",
        "9",
        "irreducible-spectrum",
        "primitive-spectrum"
      ],
      "expected_visible_count": 26,
      "bridge": "Faces and extreme dual functionals lead to pure states and representation components. Unitary-equivalence classes of irreducible representations and their kernels remain different objects; the two spectral comparisons use their respective hull–kernel topologies."
    },
    {
      "id": "g3",
      "label": "Normal parts and semilinear structure",
      "status": "ACTIVE",
      "activation_allowed": true,
      "terminal_node_ids": [
        "27",
        "28",
        "29",
        "30",
        "31",
        "32",
        "33",
        "34",
        "35",
        "36",
        "37",
        "38",
        "39",
        "40",
        "41",
        "42"
      ],
      "expected_visible_ids": [
        "1",
        "12",
        "13",
        "14",
        "15",
        "16",
        "19",
        "2",
        "27",
        "28",
        "29",
        "3",
        "30",
        "31",
        "32",
        "33",
        "34",
        "35",
        "36",
        "37",
        "38",
        "39",
        "4",
        "40",
        "41",
        "42",
        "5",
        "6",
        "7",
        "8"
      ],
      "expected_visible_count": 30,
      "bridge": "Pass from a representation component to its coefficient-kernel normal part with relative closure. Projective parametrization is a bijection. The same map, its inverse, the scalar automorphism and global orientation retain the hypotheses specified in each manuscript; full continuity requires extra conditions."
    },
    {
      "id": "g4",
      "label": "The central characterization",
      "status": "ACTIVE",
      "activation_allowed": true,
      "terminal_node_ids": [
        "43",
        "44",
        "45",
        "is-compact-operator-model"
      ],
      "expected_visible_ids": [
        "1",
        "10",
        "11",
        "12",
        "14",
        "15",
        "16",
        "18",
        "19",
        "2",
        "21",
        "22",
        "24",
        "25",
        "27",
        "29",
        "3",
        "30",
        "31",
        "32",
        "33",
        "35",
        "36",
        "37",
        "38",
        "39",
        "4",
        "40",
        "43",
        "44",
        "45",
        "5",
        "6",
        "7",
        "8",
        "9",
        "irreducible-spectrum",
        "is-compact-operator-model",
        "primitive-spectrum"
      ],
      "expected_visible_count": 39,
      "bridge": "The faithful, fully normal representation condition and continuous finite conjugation meet in the elementary-algebra characterization. Retain the same GNS model, equality of the compact-operator image, singleton condition, and two-sided conjugate continuity."
    },
    {
      "id": "g5",
      "label": "From components to classification",
      "status": "ACTIVE",
      "activation_allowed": true,
      "terminal_node_ids": [
        "46",
        "47",
        "48",
        "49",
        "50",
        "51",
        "52",
        "53",
        "54"
      ],
      "expected_visible_ids": [
        "1",
        "10",
        "11",
        "12",
        "14",
        "15",
        "16",
        "18",
        "19",
        "2",
        "21",
        "22",
        "24",
        "25",
        "27",
        "28",
        "29",
        "3",
        "30",
        "31",
        "32",
        "33",
        "35",
        "36",
        "37",
        "38",
        "39",
        "4",
        "40",
        "46",
        "47",
        "48",
        "49",
        "5",
        "50",
        "51",
        "52",
        "53",
        "54",
        "6",
        "7",
        "8",
        "9",
        "irreducible-spectrum",
        "is-compact-operator-model",
        "primitive-spectrum"
      ],
      "expected_visible_count": 46,
      "bridge": "Use compact comparisons to read representation-theoretic conditions. Compact containment differs from equality; prescribed dimension differs from an upper bound. Transport through a specified homeomorphism retains that specified map."
    },
    {
      "id": "g6",
      "label": "Compact representations, decomposition and rigidity",
      "status": "ACTIVE",
      "activation_allowed": true,
      "terminal_node_ids": [
        "55",
        "56",
        "57",
        "58",
        "59",
        "60",
        "61",
        "c0-direct-sum",
        "compact-c0-sum-equivalence",
        "compact-model-space",
        "compact-operator-c0-sum",
        "ideal-c0-sum-equivalence"
      ],
      "expected_visible_ids": [
        "1",
        "10",
        "11",
        "12",
        "14",
        "15",
        "16",
        "18",
        "19",
        "2",
        "21",
        "22",
        "23",
        "24",
        "25",
        "26",
        "27",
        "28",
        "29",
        "3",
        "30",
        "31",
        "32",
        "33",
        "35",
        "36",
        "37",
        "38",
        "39",
        "4",
        "40",
        "42",
        "47",
        "5",
        "53",
        "55",
        "56",
        "57",
        "58",
        "59",
        "6",
        "60",
        "61",
        "7",
        "8",
        "9",
        "c0-direct-sum",
        "compact-c0-sum-equivalence",
        "compact-model-space",
        "compact-operator-c0-sum",
        "ideal-c0-sum-equivalence",
        "irreducible-spectrum",
        "is-compact-operator-model",
        "primitive-spectrum"
      ],
      "expected_visible_count": 54,
      "bridge": "Faithful compact representation leads to the canonical c₀-decomposition indexed by minimal nonzero closed ideals. Its compact-operator summands are distinct from compact operators on a Hilbert direct sum. The final rigidity results assert existence of an isomorphism, with the different model hypotheses below."
    }
  ],
  "context": {
    "reading_A": "reading-a/index.html",
    "counted_as_Card": false
  },
  "website_publication": {
    "edition": "Version 1",
    "publication_date": "2026-11-02"
  },
  "reader_pdf": {
    "url": "project.pdf",
    "edition": "Version 1",
    "bytes": {
      "bytes": 48881697,
      "sha256": "acde0149aadccbecfbe9858484347df4378b62b15a44a2222aeefb32cc7a8a41"
    }
  },
  "formal_CURRENT_changed": false
}