Goal:
  
  G : t
  HI : invariants
  HG : acyclic_no_loop
  x : VSet.elt
  y : VSet.elt
  inx : VSet.In x (V G)
  iny : VSet.In y (V G)
  zl : Z
  eq : lsp (s G) x = Some zl
  pos : 0 <= zl
  zof : Z.of_nat (to_label (lsp (s G) x)) = zl
  yx : lsp y x = None
  ============================
   True


DEBUG:Going to execute:
let rec use_hyps :=
            match goal with
            | H:_ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:(_ * _)%nat |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           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"