∀ {Γ : Type u_1} {R : Type u_2} [inst : LinearOrder Γ] [inst_1 : Zero R] [inst_2 : LinearOrder R]
  {x : Lex (HahnSeries Γ R)}
  (motive : (∃ i, (∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j) ∧ (ofLex 0).coeff i < (ofLex x).coeff i) → Prop)
  (h : ∃ i, (∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j) ∧ (ofLex 0).coeff i < (ofLex x).coeff i),
  (∀ (i : Γ) (hj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j) (hi : (ofLex 0).coeff i < (ofLex x).coeff i),
      motive ⋯) →
    motive h