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
  ============================
   (Alli
      (λ (i : nat) (x0 : A),
         ∑ y0 : B,
           (nth_error (x :: l) i = Some x0 ∧ nth_error (y :: l') i = Some y0)
           × P x0 y0) 1 l)


DEBUG:Going to execute:
fun flags =>
             match reverse goal with
             | |- ?X1 =>
                   <Coq.Init.Tauto.is_unit_or_eq> flags X1; constructor 1
             | H:?X1 |- _ => <Coq.Init.Tauto.is_empty> flags X1; elim H
             | _ => Ltac.assumption
             end