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Theorems · Theorem · ring theory

AlgEquiv.toLinearMap_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.toLinearMap x = e x
Defined in
Mathlib.Algebra.Algebra.Equiv
Cited by
2 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringSemiringAlgebraAlgebra
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Around this declaration

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

Matrix.Represents.one · cited by 1Represents.oneMatrix.Represents.mul · cited by 0Represents.mulDFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapAlgEquiv · cited by 1681AlgEquivAlgEquiv.toLinearMap · cited by 34AlgEquiv.toLinearMapAlgEquiv.toLinearMap_applyCITED BYCITES

Cites8

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Cited by2

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