Theorems · Theorem · ring theory
AlgEquiv.apply_symm_apply
∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
[inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (e : A₁ ≃ₐ[R] A₂) (x : A₂), e (e.symm x) = x- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.symmstatement · cited by 615
- Equiv.apply_symm_applyproof · cited by 346
- AlgEquiv.toEquivproof · cited by 65
Cited by67
Results whose statement or proof uses this declaration.
- IsLocalization.isLocalization_of_algEquivproof · cited by 11
- AlgHom.restrictNormal_commutesproof · cited by 9
- Algebra.FormallySmooth.of_equivproof · cited by 8
- AlgEquiv.comp_symmproof · cited by 5
- Algebra.trace_eq_of_algEquivproof · cited by 4
- AlgEquiv.eq_linearEquivConjAlgEquivproof · cited by 4
- PowerSeries.eval₂_coeproof · cited by 4
- Normal.of_algEquivproof · cited by 4
- Algebra.ZariskisMainProperty.of_finiteType_of_weaklyQuasiFiniteAtproof · cited by 3
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- adjoinRootXPowSubCEquiv_symm_eq_rootproof · cited by 2
- IsSymmetricAlgebra.equiv_symm_applyproof · cited by 2