Goal:
  
  A : Type
  B : Type
  P : nat → A → B → Type
  n : nat
  x : B
  n0 : nat
  x0 : A
  y : B
  l : list A
  r : list B
  r0 : P n0 x0 y
  X : All2i P (S n0) l r
  IHX : ∑ c : A, nth_error l n = Some c × P (S n0 + n)%nat c x
  hnth : nth_error r n = Some x
  ============================
   (∑ c : A, nth_error l n = Some c × P (S (n0 + n)) c x)


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