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mark arguments implicit
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  • Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus

β€ŽMathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Range.leanβ€Ž

Lines changed: 7 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -94,8 +94,8 @@ theorem cfc_mem_elemental (f : π•œ β†’ π•œ) (a : A) :
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@[deprecated (since := "2026-03-20")] alias cfc_apply_mem_elemental := cfc_mem_elemental
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lemma cfc_mem {π•œ' S : Type*} [Monoid π•œ'] [MulAction π•œ' A] [SetLike S A] [SubringClass S A]
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[SMul π•œ π•œ'] [IsScalarTower π•œ π•œ' A] [SMulMemClass S π•œ' A] [StarMemClass S A] (s : S)
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[IsClosed (s : Set A)] (f : π•œ β†’ π•œ) (a : A) (has : a ∈ s) :
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[SMul π•œ π•œ'] [IsScalarTower π•œ π•œ' A] [SMulMemClass S π•œ' A] [StarMemClass S A] {s : S}
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[hs : IsClosed (s : Set A)] (f : π•œ β†’ π•œ) {a : A} (has : a ∈ s) :
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cfc f a ∈ s :=
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have := SMulMemClass.ofIsScalarTower S π•œ π•œ' A
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StarSubalgebra.topologicalClosure_minimal (t := .ofClass s) (by simpa) (by simpa)
@@ -210,9 +210,9 @@ theorem cfcβ‚™_mem_elemental (f : π•œ β†’ π•œ) (a : A) :
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@[deprecated (since := "2026-03-20")] alias cfcβ‚™_apply_mem_elemental := cfcβ‚™_mem_elemental
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lemma cfcβ‚™_mem {π•œ' S : Type*} [Monoid π•œ'] [MulAction π•œ' A] [SetLike S A] [NonUnitalSubringClass S A]
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[SMul π•œ π•œ'] [IsScalarTower π•œ π•œ' A] [SMulMemClass S π•œ' A] [StarMemClass S A] (s : S)
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[IsClosed (s : Set A)] (f : π•œ β†’ π•œ) (a : A)
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(has : a ∈ s) : cfcβ‚™ f a ∈ s :=
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[SMul π•œ π•œ'] [IsScalarTower π•œ π•œ' A] [SMulMemClass S π•œ' A] [StarMemClass S A] {s : S}
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[hs : IsClosed (s : Set A)] (f : π•œ β†’ π•œ) {a : A} (has : a ∈ s) :
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cfcβ‚™ f a ∈ s :=
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have := SMulMemClass.ofIsScalarTower S π•œ π•œ' A
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NonUnitalStarSubalgebra.topologicalClosure_minimal (t := .ofClass s) _ (by simpa) (by simpa)
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(cfcβ‚™_mem_elemental f a)
@@ -249,8 +249,8 @@ lemma range_cfcβ‚™_nnreal_subset
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exact Set.image_mono fun _ ↦ cfcβ‚™_nonneg
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set_option backward.isDefEq.respectTransparency false in
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lemma range_cfcβ‚™_nnreal
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[NonUnitalClosedEmbeddingContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (a : A) (ha : 0 ≀ a := by cfc_tac) :
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lemma range_cfcβ‚™_nnreal [NonUnitalClosedEmbeddingContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
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(a : A) (ha : 0 ≀ a := by cfc_tac) :
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Set.range (cfcβ‚™ (R := ℝβ‰₯0) Β· a) = {x | x ∈ NonUnitalStarAlgebra.elemental ℝ a ∧ 0 ≀ x} := by
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rw [range_cfcβ‚™_nnreal_eq_image_cfcβ‚™_real a ha, Set.setOf_and, SetLike.setOf_mem_eq,
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← range_cfcβ‚™ _ ha.isSelfAdjoint, Set.inter_comm, ← Set.image_preimage_eq_inter_range]

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