Theorems · Theorem · functional analysis
cfc.congr_simp
∀ {R : Type u_3} {A : Type u_4} {p p_1 : A → Prop} (e_p : p = p_1) [inst : CommSemiring R] [inst_1 : StarRing R]
[inst_2 : MetricSpace R] [inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : TopologicalSpace A]
[inst_6 : Ring A] [inst_7 : StarRing A] [inst_8 : Algebra R A] [instCFC : ContinuousFunctionalCalculus R A p]
(f f_1 : R → R), f = f_1 → ∀ (a a_1 : A), a = a_1 → cfc f a = cfc f_1 a_1- Cited by
- 16 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousStarstatement and proof · cited by 543
- IsTopologicalSemiringstatement and proof · cited by 442
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- cfcstatement and proof · cited by 228
Cited by16
Results whose statement or proof uses this declaration.
- CFC.rpow_zeroproof · cited by 8
- cfc_apply_oneproof · cited by 5
- cfc_apply_zeroproof · cited by 4
- apply_le_nnnorm_cfc_nnrealproof · cited by 3
- CFC.rpow_oneproof · cited by 3
- cfc_im_idproof · cited by 3
- cfc_zpowproof · cited by 2
- cfc_map_polynomialproof · cited by 1
- argSelfAdjoint_expUnitaryproof · cited by 0
- cfc_eval_Cproof · cited by 0
- cfc_eval_Xproof · cited by 0
- cfc_map_divproof · cited by 0