Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  n : Z
  x : V.t
  e : EdgeSet.elt
  Hle : leq_vertices G n x e..s
  Vy : ~ VSet.In e..s (V G)
  H : EdgeSet.In e (E G)
  ============================
   (EdgeSet.In e (E G))


DEBUG:Going to execute:
let rec use_hyp H :=
            match type of H with
            | _ /\ _ => exact H || destruct_hyp H
            | (_ * _)%nat => exact H || destruct_hyp H
            | _ => try (solve [ inversion H ])
            end
           with do_intro := let H := fresh in
                            intro H; use_hyp H
           with destruct_hyp H := case H; clear H; do_intro; do_intro
           in
           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"