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  "assumptions": "Let A be a nonzero unital complex C*-algebra, H a separable complex Hilbert space, and π a unital representation of A on H that is a representative of the unique unitary-equivalence class of nonzero irreducible representations of A.",
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      "label": "MathlibAnnex.Analysis.CStarAlgebra.Representation.IsSingletonIrreducibleModelAmongNonUnital",
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      "text": "Exact formal dependency; inspect the linked Card and exact source."
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  "conclusion": "H is finite-dimensional over ℂ.",
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  "name": "MathlibAnnex.Analysis.CStarAlgebra.Representation.finiteDimensional_space_of_singleton_amongNonUnital",
  "natural_language_statement": "Let A be a nonzero unital complex C*-algebra, H a separable complex Hilbert space, and π a unital representation of A on H that is a representative of the unique unitary-equivalence class of nonzero irreducible representations of A. Then H is finite-dimensional over ℂ.",
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      "text": "Exact Lean statement: ∀ {A : Type u} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {H : Type v} [inst_3 : NormedAddCommGroup H] [inst_4 : InnerProductSpace ℂ H] [inst_5 : CompleteSpace H] [Nontrivial A] [TopologicalSpace.SeparableSpace H] (pi : MathlibAnnex.Analysis.CStarAlgebra.Representation A H), pi.IsSingletonIrreducibleModelAmongNonUnital → FiniteDimensional ℂ H"
    },
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      "step_id": "source_equation",
      "text": "FiniteDimensional ℂ H."
    },
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      "text": "The source passes from the nonunital-interface formulation of the unique-class condition to its unital formulation and applies the finite-dimensional-space theorem, whose compact-identity route yields the result."
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  ],
  "proof_summary": "The source passes from the nonunital-interface formulation of the unique-class condition to its unital formulation and applies the finite-dimensional-space theorem, whose compact-identity route yields the result.",
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    "text": "theorem finiteDimensional_space_of_singleton_amongNonUnital\n    [Nontrivial A] [TopologicalSpace.SeparableSpace H]\n    (pi : Representation A H)\n    (hsingle : IsSingletonIrreducibleModelAmongNonUnital.{u, v, u} pi) :\n    FiniteDimensional ℂ H"
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