{M : Type u_1} →
  [inst : CommGroup M] →
    [inst_1 : LinearOrder M] →
      [inst_2 : IsOrderedMonoid M] →
        {α : Type u_2} →
          (f : M → α) →
            (∀ (a b : M), MulArchimedeanClass.mk a = MulArchimedeanClass.mk b → f a = f b) → MulArchimedeanClass M → α