∀ (R : Type u_1) {M : Type u_3} {N : Type u_4} [inst : CommSemiring R] [inst_1 : AddMonoid M] [inst_2 : AddMonoid N]
  (f : M →+ N) (a : AddMonoidAlgebra R M),
  (AddMonoidAlgebra.mapDomainBialgHom R f) a = AddMonoidAlgebra.mapDomain (⇑f) a