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


DEBUG:Going to execute:
let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); try arith_congr;
             (solve [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"