Goal:
  
  A : Type
  B : Type
  P : nat → A → B → Type
  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 : ∀ n : nat,
          nth_error l n = Some x0
          → ∑ c : B, nth_error r n = Some c × P (S n0 + n)%nat x0 c
  ============================
   (P n0 x0 y)


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