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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. No additional hypotheses are supplied to this theorem. Its proof uses the previously constructed faithful representation on the separable CAR trace-GNS space.",
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      "text": "/-- The existing faithful separable representation bounds the fixed carrier. -/\ntheorem cardinalMk_atomicCounterexampleAlgebra_le_continuum :\n    #AtomicCounterexampleAlgebra ≤ Cardinal.continuum := by\n  letI : TopologicalSpace.SeparableSpace SeparableCounterexampleHilbertSpace :=\n    separableSpace_separableCounterexampleHilbertSpace\n  exact Representation.cardinalMk_le_continuum_of_injective\n    separableCounterexampleRepresentation separableCounterexampleRepresentation_injective"
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