Theorems · Definition · group theory

DistribMulActionHom.casesOn

{M : Type u_1} →
  [inst : Monoid M] →
    {N : Type u_2} →
      [inst_1 : Monoid N] →
        {φ : M →* N} →
          {A : Type u_10} →
            [inst_2 : AddMonoid A] →
              [inst_3 : DistribMulAction M A] →
                {B : Type u_11} →
                  [inst_4 : AddMonoid B] →
                    [inst_5 : DistribMulAction N B] →
                      {motive : (A →ₑ+[φ] B) → Sort u} →
                        (t : A →ₑ+[φ] B) →
                          ((toMulActionHom : A →ₑ[⇑φ] B) →
                              (map_zero' : toMulActionHom.toFun 0 = 0) →
                                (map_add' :
                                    ∀ (x y : A),
                                      toMulActionHom.toFun (x + y) = toMulActionHom.toFun x + toMulActionHom.toFun y) →
                                  motive
                                    { toMulActionHom := toMulActionHom, map_zero' := map_zero',
                                      map_add' := map_add' }) →
                            motive t

Defined in

Mathlib.GroupTheory.GroupAction.Hom

Cited by

1 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

MonoidMonoidAddMonoidDistribMulActionAddMonoidDistribMulAction