∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {α : Type u_2}
  (f : M → α) (h : ∀ (a b : M), ArchimedeanClass.mk a = ArchimedeanClass.mk b → f a = f b) (a : M),
  ArchimedeanClass.lift f h (ArchimedeanClass.mk a) = f a