Goal:
  
  A : Type
  P : list A → Type
  X : P []
  X0 : ∀ (l : list A) (x : A), P (l ++ [x])
  l : list A
  ============================
   (P [])


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"