Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  l0 : list A
  IHHF : Alli
           (λ (i : nat) (x : A),
              ∑ y : B,
                (nth_error l0 i = Some x ∧ nth_error l' i = Some y) × P x y)
           0 l
  ============================
   (Alli
      (λ (x : nat) (x0 : A),
         ∑ y : B,
           (nth_error l0 x = Some x0 ∧ nth_error l' x = Some y) × P x0 y) 0 l)


DEBUG:Going to execute:
solve
[ trivial
with eq_true
| reflexivity
| symmetry; trivial
| contradiction
| congruence ]