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      "label": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.IsIrreducible",
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  "conclusion": "The representation π is a representative of the unique unitary-equivalence class of nonzero irreducible representations of A: π is nonzero and irreducible, and every nonzero irreducible representation of A on any complex Hilbert space is unitarily equivalent to π. The definition does not assume faithfulness or separability of A or H.",
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  "name": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.IsSingletonIrreducibleModel",
  "natural_language_statement": "Let A be a complex C*-algebra, not assumed unital, H a complex Hilbert space, and π a representation of A on H. The representation π is a representative of the unique unitary-equivalence class of nonzero irreducible representations of A: π is nonzero and irreducible, and every nonzero irreducible representation of A on any complex Hilbert space is unitarily equivalent to π. The definition does not assume faithfulness or separability of A or H.",
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      "text": "IsSingletonIrreducibleModel π ↔ IsIrreducible π ∧ ∀ K ρ, IsIrreducible ρ → UnitaryEquivalent π ρ."
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      "text": "Unfold the source predicate and its irreducibility/equivalence definitions. The definition-level K is independently quantified; later uses specialize universes as {u,v,u} rather than asserting this is the full ConstantInfo parameter order."
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    "text": "def IsSingletonIrreducibleModel\n    (pi : NonUnitalCStarRepresentation A H) : Prop"
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