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