@@ -94,8 +94,8 @@ theorem cfc_mem_elemental (f : π β π) (a : A) :
9494@ [deprecated (since := "2026-03-20" )] alias cfc_apply_mem_elemental := cfc_mem_elemental
9595
9696lemma cfc_mem {π' S : Type *} [Monoid π'] [MulAction π' A] [SetLike S A] [SubringClass S A]
97- [SMul π π'] [IsScalarTower π π' A] [SMulMemClass S π' A] [StarMemClass S A] ( s : S)
98- [IsClosed (s : Set A)] (f : π β π) ( a : A) (has : a β s) :
97+ [SMul π π'] [IsScalarTower π π' A] [SMulMemClass S π' A] [StarMemClass S A] { s : S}
98+ [hs : IsClosed (s : Set A)] (f : π β π) { a : A} (has : a β s) :
9999 cfc f a β s :=
100100 have := SMulMemClass.ofIsScalarTower S π π' A
101101 StarSubalgebra.topologicalClosure_minimal (t := .ofClass s) (by simpa) (by simpa)
@@ -210,9 +210,9 @@ theorem cfcβ_mem_elemental (f : π β π) (a : A) :
210210@ [deprecated (since := "2026-03-20" )] alias cfcβ_apply_mem_elemental := cfcβ_mem_elemental
211211
212212lemma cfcβ_mem {π' S : Type *} [Monoid π'] [MulAction π' A] [SetLike S A] [NonUnitalSubringClass S A]
213- [SMul π π'] [IsScalarTower π π' A] [SMulMemClass S π' A] [StarMemClass S A] ( s : S)
214- [IsClosed (s : Set A)] (f : π β π) ( a : A)
215- (has : a β s) : cfcβ f a β s :=
213+ [SMul π π'] [IsScalarTower π π' A] [SMulMemClass S π' A] [StarMemClass S A] { s : S}
214+ [hs : IsClosed (s : Set A)] (f : π β π) { a : A} (has : a β s) :
215+ cfcβ f a β s :=
216216 have := SMulMemClass.ofIsScalarTower S π π' A
217217 NonUnitalStarSubalgebra.topologicalClosure_minimal (t := .ofClass s) _ (by simpa) (by simpa)
218218 (cfcβ_mem_elemental f a)
@@ -249,8 +249,8 @@ lemma range_cfcβ_nnreal_subset
249249 exact Set.image_mono fun _ β¦ cfcβ_nonneg
250250
251251set_option backward.isDefEq.respectTransparency false in
252- lemma range_cfcβ_nnreal
253- [NonUnitalClosedEmbeddingContinuousFunctionalCalculus β A IsSelfAdjoint] (a : A) (ha : 0 β€ a := by cfc_tac) :
252+ lemma range_cfcβ_nnreal [NonUnitalClosedEmbeddingContinuousFunctionalCalculus β A IsSelfAdjoint]
253+ (a : A) (ha : 0 β€ a := by cfc_tac) :
254254 Set.range (cfcβ (R := ββ₯0 ) Β· a) = {x | x β NonUnitalStarAlgebra.elemental β a β§ 0 β€ x} := by
255255 rw [range_cfcβ_nnreal_eq_image_cfcβ_real a ha, Set.setOf_and, SetLike.setOf_mem_eq,
256256 β range_cfcβ _ ha.isSelfAdjoint, Set.inter_comm, β Set.image_preimage_eq_inter_range]
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