Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  d : A
  Γ0 : list A
  a : 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
                × All2_fold P (skipn (S n) Γ) (skipn (S n) Γ')
                  × P (skipn (S n) Γ) (skipn (S n) Γ') d d'
  Hrel : All2_fold P Γ0 Γ'
  p : P Γ0 Γ' d a
  H : nth_error Γ' n = Some d'
  x : A
  a0 : nth_error Γ0 n = Some x
  a1 : All2_fold P (skipn (S n) Γ0) (skipn (S n) Γ')
  b0 : P (skipn (S n) Γ0) (skipn (S n) Γ') x d'
  ============================
   (nth_error Γ0 n = Some ?d@{p0:=(a0, (a1, b0))})


DEBUG:Going to execute:
match reverse goal with
           | id:(?X1 → ?X2) → ?X3
             |- _ =>
                 Ltac.cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | Ltac.cut (X1 → X2);
                     [ exact
                     id
                     | generalize (λ y : X2, id (λ x : X1, y)); intro; clear
                        id; (solve [ t_tauto_intuit ]) ] ]
           | id:¬ ?X1 → ?X3
             |- _ =>
                 Ltac.cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | Ltac.cut (¬ X1);
                     [ exact
                     id
                     | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
           | |- ?X1 =>
                 <Coq.Init.Tauto.is_disj> flags X1; (solve
                  [ Ltac.left; t_tauto_intuit | Ltac.right; t_tauto_intuit ])
           end