Theorems · Theorem · ring theory
AlgEquiv.coe_coe_symm_apply_coe_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] {F : Type u_1} [inst_5 : EquivLike F A₁ A₂]
[inst_6 : AlgEquivClass F R A₁ A₂] (f : F) (x : A₁), (↑f).symm (f x) = x- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 1 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.
Cites10
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 · cited by 1,681
- AlgEquiv.symmstatement · cited by 615
- EquivLikestatement and proof · cited by 165
- AlgEquivClassstatement and proof · cited by 17
- AlgEquivClass.toAlgEquivstatement · cited by 12
- EquivLike.left_invproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- AlgEquiv.spectrum_eqproof · cited by 9