∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {N : Type u_2}
  [inst_3 : AddCommGroup N] [inst_4 : LinearOrder N] [inst_5 : IsOrderedAddMonoid N] (f : M →+o N) (a : M),
  (ArchimedeanClass.orderHom f) (ArchimedeanClass.mk a) = ArchimedeanClass.mk (f a)