∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] {f g : CauSeq α abs}
  (motive : (∃ i, ∀ j ≥ i, ↑f j ≤ ↑g j) → Prop) (h : ∃ i, ∀ j ≥ i, ↑f j ≤ ↑g j),
  (∀ (i : ℕ) (hi : ∀ j ≥ i, ↑f j ≤ ↑g j), motive ⋯) → motive h