Theorems · Theorem · ring theory
AlgEquiv.symm_apply_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 : A₁), e.symm (e x) = x- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 36 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.symm_apply_applyproof · cited by 320
- AlgEquiv.toEquivproof · cited by 65
Cited by36
Results whose statement or proof uses this declaration.
- AlgEquiv.symm_compproof · cited by 7
- Algebra.FormallySmooth.of_comp_surjectiveproof · cited by 6
- Ideal.Fiber.exists_smul_eq_one_tmulproof · cited by 3
- KaehlerDifferential.tensorKaehlerEquiv_tmul_Dproof · cited by 3
- isIntegral_algEquivproof · cited by 3
- Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_valproof · cited by 2
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- FiniteField.exists_forall_apply_eq_powproof · cited by 1
- map_equiv_traceDualproof · cited by 1
- IsAdjoinRoot.algEquiv_algEquivproof · cited by 1
- AlgEquiv.isTranscendenceBasisproof · cited by 1
- AlgEquiv.isTranscendenceBasis_iffproof · cited by 1