∀ (Γ : Type u_1) (R : Type u_2) [inst : LinearOrder Γ] [inst_1 : LinearOrder R] [inst_2 : AddCommGroup R]
  [inst_3 : IsOrderedAddMonoid R] (a : Lex (HahnSeries Γ R)) (ha : a ≠ 0) (b : Lex (HahnSeries Γ R)) (hb : b ≠ 0),
  FiniteArchimedeanClass.mk ↑⟨a, ha⟩ ⋯ ≤ FiniteArchimedeanClass.mk ↑⟨b, hb⟩ ⋯ →
    (fun x =>
          match x with
          | ⟨x, hx⟩ => toLex ((ofLex x).orderTop.untop ⋯, FiniteArchimedeanClass.mk (ofLex x).leadingCoeff ⋯))
        ⟨a, ha⟩ ≤
      (fun x =>
          match x with
          | ⟨x, hx⟩ => toLex ((ofLex x).orderTop.untop ⋯, FiniteArchimedeanClass.mk (ofLex x).leadingCoeff ⋯))
        ⟨b, hb⟩