Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  a : A
  Γ : list A
  d' : A
  Γ'0 : 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 Γ Γ'0
  p : P Γ Γ'0 a d'
  H : nth_error Γ n = Some d
  x : A
  p0 : nth_error Γ'0 n = Some x
       × All2_fold P (skipn (S n) Γ) (skipn (S n) Γ'0)
         × P (skipn (S n) Γ) (skipn (S n) Γ'0) d x
  ============================
   (nth_error Γ'0 n = Some ?d'
    × All2_fold P (skipn (S (S n)) (a :: Γ)) (skipn (S (S n)) (d' :: Γ'0))
      × P (skipn (S (S n)) (a :: Γ)) (skipn (S (S n)) (d' :: Γ'0)) d ?d')


DEBUG:Going to execute:
match reverse goal with
           | id:?X1
             |- _ =>
                 <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro;
                  clear id
           | id:_ ↔ _ |- _ => elim id; do 2 intro; clear id
           | id:¬ _ |- _ => red in id
           | id:?X1
             |- _ =>
                 <Coq.Init.Tauto.is_disj> flags X1; elim id; intro; clear id
           | _ =>
               <Coq.Init.Tauto.find_cut>
                ltac:(fun id0 id1 X2 =>
                        assert X2; [ exact (id0 id1) | clear id0 ])
           | id:?X1 → ?X2
             |- _ =>
                 <Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
                  [ intro; clear id
                  | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
           | id:?X1 → ?X2
             |- _ =>
                 <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2 id
           | id:?X1 ↔ ?X2 → ?X3
             |- _ =>
                 assert ((X1 → X2) → (X2 → X1) → X3) by
                  (do 2 intro; apply id; Ltac.split; Ltac.assumption); clear
                  id
           | id:?X1 → ?X2
             |- _ =>
                 <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2 id
           | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; Ltac.split
           | |- _ ↔ _ => Ltac.split
           | |- ¬ _ => red
           end; <Coq.Init.Tauto.not_dep_intros>