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    "assumptions": "Let A ⊆ B(Hₐₜ) be the fixed unital C*-algebra obtained by adjoining the chosen shell-link unitaries to the atomic representation of the CAR algebra C, and then taking the norm-closed unital *-algebra they generate. Let D ⊆ A and assume that D is dense in the norm topology of A.",
    "conclusion": "𝔠 ≤ |D|. In particular, A has no countable norm-dense subset.",
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      "text": "/-- No norm-dense subset of the fixed algebra is smaller than the continuum. -/\ntheorem continuum_le_cardinalMk_dense_atomicCounterexampleAlgebra\n    (s : Set AtomicCounterexampleAlgebra) (hs : Dense s) :\n    Cardinal.continuum ≤ #s :=\n  Representation.continuum_le_cardinalMk_dense_algebra_of_singleton_of_not_finiteDimensional\n    (shellFamilyInclusion homogeneityShellFamily)\n    (isUniqueIrreducibleModel_shellFamilyInclusion.{0} homogeneityShellFamily).2\n    (not_finiteDimensional_shellFamilyTarget homogeneityShellFamily) s hs"
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