Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  a : A
  Γ : list A
  Γ' : list A
  d : A
  IHn : ∀ (Γ Γ' : list A) (d : A),
          All2_fold P Γ Γ'
          → nth_error Γ n = Some d
            → ∑ d' : A,
                nth_error Γ' n = Some d'
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P (a :: Γ) Γ'
  Hrel0 := {| pr1 := {| pr1 := a :: Γ; pr2 := Γ' |}; pr2 := Hrel |}
        : sigma
            (λ index : sigma (λ _ : list A, list A),
               All2_fold P (pr1 index) (pr2 index))
  ============================
   (let H := CoreTactics.block in
    nth_error (a :: Γ) (S n) = Some d
    → let H0 := CoreTactics.block in
      ∑ d' : A,
        nth_error Γ' (S n) = Some d'
        × (let Γs := skipn (S (S n)) (a :: Γ) in
           let Γs' := skipn (S (S n)) Γ' in
           All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
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