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
  a0 : nth_error Γ'0 n = Some x
  a1 : All2_fold P (skipn (S n) Γ) (skipn (S n) Γ'0)
  b0 : P (skipn (S n) Γ) (skipn (S n) Γ'0) d x
  ============================
   (nth_error Γ'0 n = Some ?d'@{p0:=(a0, (a1, b0))}
    × 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'@{p0:=(a0, (a1, b0))})


DEBUG:Going to execute:
<Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
            [ intro; clear id
            | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 1: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 2: Backtrace:

Not convertible.
Level 2: Backtrace:

Not convertible.
Level 2: Backtrace:

Not convertible.
Level 1: Backtrace:

Not convertible.