Theorems · Theorem · functional analysis
cfc_comp_neg
∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : CommRing R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
[inst_3 : IsTopologicalRing R] [inst_4 : ContinuousStar R] [inst_5 : TopologicalSpace A] [inst_6 : Ring A]
[inst_7 : StarRing A] [inst_8 : Algebra R A] [inst_9 : ContinuousFunctionalCalculus R A p] (f : R → R) (a : A)
[ContinuousMap.UniqueHom R A],
autoParam (ContinuousOn f ((fun x => -x) '' spectrum R a)) cfc_comp_neg._auto_1 →
autoParam (p a) cfc_comp_neg._auto_3 → cfc (fun x => f (-x)) a = cfc f (-a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.imagestatement and proof · cited by 5,609
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousStarstatement and proof · cited by 543
- spectrumstatement and proof · cited by 510
- IsTopologicalRingstatement and proof · cited by 402
- ContinuousFunctionalCalculusstatement and proof · cited by 331
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