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