∀ {α : Type u_2} {β : α → Type u_1} (a : α) (x : { s // s.fst = a }) (a_1 : Sigma β) (h : a_1.fst = a),
  (fun b => ⟨⟨a, b⟩, ⋯⟩)
      ((fun x =>
          match x with
          | ⟨⟨fst, b⟩, h⟩ => h ▸ b)
        ⟨a_1, h⟩) =
    ⟨a_1, h⟩