∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M]
  {p : ArchimedeanClass M → Prop}, (∀ (A : ArchimedeanClass M), p A) ↔ ∀ (a : M), p (ArchimedeanClass.mk a)