Goal:
  
  A : Type
  f : A → A
  x : A
  l : list A
  p : f x = x
  X : All (λ x : A, f x = x) l
  IHX : map f l = l
  ============================
   (x :: l = x :: l)


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"