Theorems · Definition · nonassociative algebras

NonUnitalAlgHom.casesOn

{R : Type u} →
  {S : Type u₁} →
    [inst : Monoid R] →
      [inst_1 : Monoid S] →
        {φ : R →* S} →
          {A : Type v} →
            {B : Type w} →
              [inst_2 : NonUnitalNonAssocSemiring A] →
                [inst_3 : DistribMulAction R A] →
                  [inst_4 : NonUnitalNonAssocSemiring B] →
                    [inst_5 : DistribMulAction S B] →
                      {motive : (A →ₛₙₐ[φ] B) → Sort u_1} →
                        (t : A →ₛₙₐ[φ] B) →
                          ((toDistribMulActionHom : A →ₑ+[φ] B) →
                              (map_mul' :
                                  ∀ (x y : A),
                                    toDistribMulActionHom.toFun (x * y) =
                                      toDistribMulActionHom.toFun x * toDistribMulActionHom.toFun y) →
                                motive { toDistribMulActionHom := toDistribMulActionHom, map_mul' := map_mul' }) →
                            motive t

Defined in

Mathlib.Algebra.Algebra.NonUnitalHom

Cited by

1 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

MonoidMonoidNonUnitalNonAssocSemiringDistribMulActionNonUnitalNonAssocSemiringDistribMulAction