∀ {a b c : ℕ} (motive : (∃ k, a - b + k = c) → a ≤ b ∨ b ≤ a → Prop) (x : ∃ k, a - b + k = c) (x_1 : a ≤ b ∨ b ≤ a),
  (∀ (x : ∃ k, a - b + k = c) (hle : a ≤ b), motive x ⋯) →
    (∀ (d : ℕ) (hd : a - b + d = c) (hge : b ≤ a), motive ⋯ ⋯) → motive x x_1