Theorems · Theorem · functional analysis

cfcHomSuperset.congr_simp

∀ {R : Type u_1} {A : Type u_2} {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 : Ring A]
  [inst_6 : StarRing A] [inst_7 : TopologicalSpace A] [inst_8 : Algebra R A]
  [instCFC : ContinuousFunctionalCalculus R A p] {a a_1 : A} (e_a : a = a_1) (ha : p a) {s : Set R}
  (hs : spectrum R a ⊆ s), cfcHomSuperset ha hs = cfcHomSuperset ⋯ ⋯

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingMetricSpaceIsTopologicalSemiringContinuousStarRingStarRingTopologicalSpaceAlgebraContinuousFunctionalCalculus