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:
<Coq.Init.Tauto.is_empty> flags X1; elim H
Level 2: Backtrace:

In environment
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'
Unable to unify "Some ?d@{p0:=(a0, (a1, b0))}" with
 "(fix nth_error (l : list A) (n : nat) {struct n} : option A :=
     match n with
     | 0 => match l with
            | [] => None
            | x :: _ => Some x
            end
     | S n0 => match l with
               | [] => None
               | _ :: l0 => nth_error l0 n0
               end
     end) Γ0 n".
Level 2: Backtrace:

In environment
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'
Unable to unify "Some ?d@{p0:=(a0, (a1, b0))}" with
 "(fix nth_error (l : list A) (n : nat) {struct n} : option A :=
     match n with
     | 0 => match l with
            | [] => None
            | x :: _ => Some x
            end
     | S n0 => match l with
               | [] => None
               | _ :: l0 => nth_error l0 n0
               end
     end) Γ0 n".
Level 3: Backtrace:

In environment
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'
Unable to unify "Some ?d@{p0:=(a0, (a1, b0))}" with
 "(fix nth_error (l : list A) (n : nat) {struct n} : option A :=
     match n with
     | 0 => match l with
            | [] => None
            | x :: _ => Some x
            end
     | S n0 => match l with
               | [] => None
               | _ :: l0 => nth_error l0 n0
               end
     end) Γ0 n".
Level 3: Backtrace:

In environment
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'
Unable to unify "Some ?d@{p0:=(a0, (a1, b0))}" with
 "(fix nth_error (l : list A) (n : nat) {struct n} : option A :=
     match n with
     | 0 => match l with
            | [] => None
            | x :: _ => Some x
            end
     | S n0 => match l with
               | [] => None
               | _ :: l0 => nth_error l0 n0
               end
     end) Γ0 n".
Level 2: Backtrace:

In environment
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'
Unable to unify "Some ?d@{p0:=(a0, (a1, b0))}" with
 "(fix nth_error (l : list A) (n : nat) {struct n} : option A :=
     match n with
     | 0 => match l with
            | [] => None
            | x :: _ => Some x
            end
     | S n0 => match l with
               | [] => None
               | _ :: l0 => nth_error l0 n0
               end
     end) Γ0 n".
Level 2: Backtrace:

In environment
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'
Unable to unify "Some ?d@{p0:=(a0, (a1, b0))}" with
 "(fix nth_error (l : list A) (n : nat) {struct n} : option A :=
     match n with
     | 0 => match l with
            | [] => None
            | x :: _ => Some x
            end
     | S n0 => match l with
               | [] => None
               | _ :: l0 => nth_error l0 n0
               end
     end) Γ0 n".