∀ {R : Type u_2} {S : Type u_3} {M : Type u_5} {N : Type u_6} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddMonoid M] [inst_3 : AddMonoid N] (f : R →+* S) (g : M →+ N),
  (AddMonoidAlgebra.mapRangeRingHom N f).comp (AddMonoidAlgebra.mapDomainRingHom R g) =
    (AddMonoidAlgebra.mapDomainRingHom S g).comp (AddMonoidAlgebra.mapRangeRingHom M f)