∀ {R : Type u_1} {A : Type u_4} {B : Type u_5} (M : Type u_7) [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : AddMonoid M] (f : A →ₐ[R] B),
  ↑(AddMonoidAlgebra.mapRangeAlgHom M f) = AddMonoidAlgebra.mapRangeRingHom M f.toRingHom