∀ {α : Type u_1} {β : α → Type u_2}
  (motive : (x x_1 : (a : α) × β a) → (x_2 : x.fst = x_1.fst) → Eq.recOn x_2 x.snd = x_1.snd → Prop)
  (x x_1 : (a : α) × β a) (x_2 : x.fst = x_1.fst) (x_3 : Eq.recOn x_2 x.snd = x_1.snd),
  (∀ (fst : α) (snd : β fst), motive ⟨fst, snd⟩ ⟨fst, snd⟩ ⋯ ⋯) → motive x x_1 x_2 x_3