Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  ls2 : list A
  ls3 : list B
  H : [] ≠ []
  ============================
   (#|ls2| = #|ls3|)


DEBUG:Going to execute:
let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction
           | congruence ]
           in
           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"