Theorems · Theorem · functional analysis

NonUnitalStarAlgHom.restrictScalars.congr_simp

∀ (R : Type u_1) {S : Type u_2} {A : Type u_3} {B : Type u_4} [inst : Monoid R] [inst_1 : Monoid S] [inst_2 : Star A]
  [inst_3 : Star B] [inst_4 : NonUnitalNonAssocSemiring A] [inst_5 : NonUnitalNonAssocSemiring B]
  [inst_6 : MulAction R S] [inst_7 : DistribMulAction S A] [inst_8 : DistribMulAction S B]
  [inst_9 : DistribMulAction R A] [inst_10 : DistribMulAction R B] [inst_11 : IsScalarTower R S A]
  [inst_12 : IsScalarTower R S B] (f f_1 : A →⋆ₙₐ[S] B),
  f = f_1 → NonUnitalStarAlgHom.restrictScalars R f = NonUnitalStarAlgHom.restrictScalars R f_1

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses no axioms

Assumes

MonoidMonoidStarStarNonUnitalNonAssocSemiringNonUnitalNonAssocSemiringMulActionDistribMulActionDistribMulActionDistribMulActionDistribMulActionIsScalarTowerIsScalarTower