no goals
R : Type u
A : Type v
B : Type w
C : Type w₁
inst✝⁶ : Monoid R
inst✝⁵ : NonUnitalNonAssocSemiring A
inst✝⁴ : DistribMulAction R A
inst✝³ : NonUnitalNonAssocSemiring B
inst✝² : DistribMulAction R B
inst✝¹ : NonUnitalNonAssocSemiring C
inst✝ : DistribMulAction R C
f : A →ₙₐ[R] B
h₁ : ∀ (m : R) (x : A), ↑f (m • x) = m • ↑f x
h₂ : MulActionHom.toFun { toFun := ↑f, map_smul' := h₁ } 0 = 0
h₃ :
  ∀ (x y : A),
    MulActionHom.toFun { toFun := ↑f, map_smul' := h₁ } (x + y) =
      MulActionHom.toFun { toFun := ↑f, map_smul' := h₁ } x + MulActionHom.toFun { toFun := ↑f, map_smul' := h₁ } y
h₄ :
  ∀ (x y : A),
    MulActionHom.toFun
        { toMulActionHom := { toFun := ↑f, map_smul' := h₁ }, map_zero' := h₂, map_add' := h₃ }.toMulActionHom (x * y) =
      MulActionHom.toFun
          { toMulActionHom := { toFun := ↑f, map_smul' := h₁ }, map_zero' := h₂, map_add' := h₃ }.toMulActionHom x *
        MulActionHom.toFun
          { toMulActionHom := { toFun := ↑f, map_smul' := h₁ }, map_zero' := h₂, map_add' := h₃ }.toMulActionHom y
⊢ { toDistribMulActionHom := { toMulActionHom := { toFun := ↑f, map_smul' := h₁ }, map_zero' := h₂, map_add' := h₃ },
      map_mul' := h₄ } =
    f
rfl