Theorems · Theorem · ring theory
AlgEquiv.symm_apply_eq
∀ {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} {y : A₁}, e.symm x = y ↔ x = e y- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, 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
- AlgEquiv.toEquivproof · cited by 65
- Equiv.symm_apply_eqproof · cited by 63
Cited by9
Results whose statement or proof uses this declaration.
- IsIntegrallyClosed.of_equivproof · cited by 3
- PrimeSpectrum.toPiLocalization_surjective_of_discreteTopologyproof · cited by 2
- Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_applyproof · cited by 1
- StandardEtalePresentation.equivRing_xproof · cited by 1
- IntermediateField.adjoinRootEquivAdjoin_symm_apply_genproof · cited by 1
- Algebra.IsPushout.equiv_symm_algebraMap_rightproof · cited by 1
- IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_rootproof · cited by 1
- Algebra.IsPushout.equiv_symm_algebraMap_leftproof · cited by 0
- IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mkproof · cited by 0