∀ (R : Type u_4) {A : Type u_3} {B : Type u_2} (M : Type u_1) [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : Monoid M] (e : A ≃ₐ[R] B) (r : R),
  (↑↑(MonoidAlgebra.mapRangeAlgHom M ↑e).toRingHom).toFun ((algebraMap R (MonoidAlgebra A M)) r) =
    (algebraMap R (MonoidAlgebra B M)) r