{M : Type u_2} →
  [inst : CommGroup M] →
    [inst_1 : LinearOrder M] →
      [inst_2 : IsOrderedMonoid M] →
        {N : Type u_3} →
          [inst_3 : CommGroup N] →
            [inst_4 : LinearOrder N] →
              [inst_5 : IsOrderedMonoid N] → (M →*o N) → MulArchimedeanOrder M →o MulArchimedeanOrder N