(Γ : Type u_1) →
  (R : Type u_2) →
    [inst : LinearOrder Γ] →
      [inst_1 : LinearOrder R] →
        [inst_2 : AddCommGroup R] →
          [inst_3 : IsOrderedAddMonoid R] →
            Lex (Γ × FiniteArchimedeanClass R) →o FiniteArchimedeanClass (Lex (HahnSeries Γ R))