Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  H1 : sigma (λ _ : list A, list A)
  H : All2_fold P (pr1 H1) (pr2 H1)
  ============================
   (∀ Γ : list A,
      {| pr1 := Γ; pr2 := Γ |} = H1
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ0 : list A) (d : A), P Γ0 Γ0 d d) Γ)


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