Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  HF : All2 P l l'
  IHHF : Alli
           (λ (i : nat) (x : A),
              ∑ y : B,
                (nth_error l i = Some x ∧ nth_error l' i = Some y) × P x y) 0
           l
  ============================
   (nth_error (x :: l) 0 = Some x ∧ nth_error (y :: l') 0 = Some y)


DEBUG:Going to execute:
<Coq.Init.Tauto.find_cut>
            ltac:(fun id0 id1 X2 =>
                    assert X2; [ exact (id0 id1) | clear id0 ])
Level 2: evaluation returns
<coq-core.plugins.tauto::is_disj@0>
where
tauto_flags := 
of type
tauto_flags
X1 := Alli
        (λ (i : nat) (x : A),
           ∑ y : B,
             (nth_error l i = Some x ∧ nth_error l' i = Some y) × P x y) 0 l
of type
constr of type tacvalue

Level 2: Backtrace:

Tactic failure.
Level 2: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.