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


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