∀ {α : Type u_1} [inst : LinearOrder α] {a b : α} (motive : a < b ∨ a = b ∨ b < a → Prop) (x : a < b ∨ a = b ∨ b < a),
  (∀ (hlt : a < b), motive ⋯) → (∀ (HEq : a = b), motive ⋯) → (∀ (hgt : b < a), motive ⋯) → motive x