∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {N : Type u_2}
  [inst_3 : CommGroup N] [inst_4 : LinearOrder N] [inst_5 : IsOrderedMonoid N]
  (e : MulArchimedeanClass M ≃o MulArchimedeanClass N) {a b : FiniteMulArchimedeanClass M},
  ((↑e).subtypeEquiv ⋯) a ≤ ((↑e).subtypeEquiv ⋯) b ↔ a ≤ b