∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a b : M},
  ArchimedeanClass.mk a ≤ ArchimedeanClass.mk (a - b) ↔ ArchimedeanClass.mk a ≤ ArchimedeanClass.mk b