Theorems · Theorem · ring theory
AlgEquiv.autCongr_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] (ϕ : A₁ ≃ₐ[R] A₂) (ψ : A₁ ≃ₐ[R] A₁),
ϕ.autCongr ψ = ϕ.symm.trans (ψ.trans ϕ)- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- MulEquivstatement · cited by 1,142
- AlgEquiv.symmstatement · cited by 615
- AlgEquiv.transstatement · cited by 108
- AlgEquiv.autCongrstatement and proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- autEquivRootsOfUnity_apply_rootOfSplitproof · cited by 1