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
  ============================
   (∑ y0 : B,
      (nth_error (x :: l) 0 = Some x ∧ nth_error (y :: l') 0 = Some y0)
      × P x y0)


DEBUG:Going to execute:
match goal with
           | |- _ → _ => intro; t_tauto_intuit
           | |- _ => t_reduce; t_solver
           end