∀ {R : Type u_1} {A : Type u_4} {M : Type u_7} {N : Type u_8} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : AddMonoid M] [inst_4 : AddMonoid N] (e : M ≃+ N) (m : M) (a : A),
  (AddMonoidAlgebra.domCongr R A e) (AddMonoidAlgebra.single m a) = AddMonoidAlgebra.single (e m) a