∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M}
  {s : UpperSet (FiniteArchimedeanClass M)},
  a ∈ FiniteArchimedeanClass.addSubgroup s ↔ ∀ (h : a ≠ 0), FiniteArchimedeanClass.mk a h ∈ s