{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] →
                ArchimedeanClass M ≃o ArchimedeanClass N → FiniteArchimedeanClass M ≃o FiniteArchimedeanClass N