∀ {α : Type u_2} {r : α → α → Prop} {ι : Sort u_1} {f : ι → α} (a b : ι)
  (motive : (∃ z, r (f a) (f z) ∧ r (f b) (f z)) → Prop) (x : ∃ z, r (f a) (f z) ∧ r (f b) (f z)),
  (∀ (c : ι) (h₁ : r (f a) (f c)) (h₂ : r (f b) (f c)), motive ⋯) → motive x