Goal:
  
  A : Type
  P : list A → A → Type
  a : A
  Γ : list A
  Δ : list A
  IHΓ : ∀ Δ : list A,
          All_fold P (Γ ++ Δ)
          → All_fold P Δ × All_fold (λ Γ : list A, P (Γ ++ Δ)) Γ
  X : All_fold P (a :: Γ ++ Δ)
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    All_fold (λ Γ : list A, P (Γ ++ Δ)) (a :: Γ))


DEBUG:Going to execute:
let id' := fresh id in
           get_signature_pack id id'; hnf in (value of id');
            hnf in (type of id');
            lazymatch goal with
            | id':=?v:_
              |- context [ id ] =>
                  generalize (eq_refl : v = id'); clearbody id'; simpl in id';
                   cont id id' id v
            | id':=?v:_
              |- _ =>
                  let id'1 := fresh id' in
                  let id'2 := fresh id' in
                  set (id'2 := pr2 id'); set (id'1 := pr1 id') in id'2;
                   hnf in (value of id'1), (value of id'2);
                   try red in (type of id'2);
                   match goal with
                   | id'1:=?t:_
                     |- _ =>
                         generalize (eq_refl : t = id'1); clearbody id'2 id'1;
                          clear id' id; try unfold signature in id'2;
                          hnf in id'2; simpl in id'2; rename id'2 into id;
                          cont id id id'1 t
                   end
            end