∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {N : Type u_2}
  [inst_3 : AddCommGroup N] [inst_4 : LinearOrder N] [inst_5 : IsOrderedAddMonoid N]
  (e : ArchimedeanClass M ≃o ArchimedeanClass N),
  (FiniteArchimedeanClass.congrOrderIso e).symm = FiniteArchimedeanClass.congrOrderIso e.symm