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Theorems · Theorem · ring theory

AlgEquiv.one_apply

∀ {R : Type uR} {A₁ : Type uA₁} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Algebra R A₁] (x : A₁), 1 x = x
Defined in
Mathlib.Algebra.Algebra.Equiv
Cited by
3 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IntermediateField.restrictNormalHom_ker · cited by 1IntermediateField.restric…InfiniteGalois.fixingSubgroup_fixedField · cited by 0InfiniteGalois.fixingSubg…IsGalois.normalBasis_apply · cited by 0IsGalois.normalBasis_applyDFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringAlgEquiv · cited by 1681AlgEquivAlgEquiv.one_applyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.