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Theorems · Theorem · ring theory

StarAlgEquiv.symm_apply_apply

∀ {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : Add A] [inst_1 : Add B] [inst_2 : Mul A] [inst_3 : Mul B]
  [inst_4 : SMul R A] [inst_5 : SMul R B] [inst_6 : Star A] [inst_7 : Star B] (e : A ≃⋆ₐ[R] B) (x : A), e.symm (e x) = x
Defined in
Mathlib.Algebra.Star.StarAlgHom
Cited by
5 results in Mathlib
Foundations
Depth 21 from the axioms · uses Quot.sound
Assumes
AddAddMulMulSMulSMulStarStar
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

StarAlgEquiv.nnnorm_map · cited by 1StarAlgEquiv.nnnorm_mapcontinuousFunctionalCalculus_map_id · cited by 1continuousFunctionalCalcu…StarAlgEquiv.arrowCongr'_comp · cited by 0StarAlgEquiv.arrowCongr'_…StarAlgEquiv.arrowCongr_comp · cited by 0StarAlgEquiv.arrowCongr_c…CompletelyPositiveMap.map_cstarMatrix_nonneg · cited by 0CompletelyPositiveMap.map…DFunLike.coe · cited by 62936DFunLike.coeStar · cited by 496StarStarAlgEquiv · cited by 132StarAlgEquivStarAlgEquiv.symm · cited by 49StarAlgEquiv.symmStarAlgEquiv.toStarRingEquiv · cited by 14StarAlgEquiv.toStarRingEq…StarRingEquiv.symm_apply_apply · cited by 1StarRingEquiv.symm_apply_…StarAlgEquiv.symm_apply_applyCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.