Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1 : sigma (λ _ : list A, list A)
  h : All2_fold Q (pr1 h1) (pr2 h1)
  ============================
   ({| pr1 := []; pr2 := [] |} = h1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])


DEBUG:Going to execute:
fun id id' =>
             hnf in id;
              match type of id with
              | sigma _ =>
                  let xn := fresh id "'" in
                  destruct id as [xn id]; DepElim.decompose_exists xn id;
                   cbv beta iota delta [TODO projection TODO projection]
                    in id, id'; DepElim.decompose_exists id id'
              | _ =>
                  cbv beta iota delta [TODO projection TODO projection]
                   in id, id'
              end