Goal:
  
  G : t
  s1 : VSet.t
  s' : VSet.t
  x0 : V.t
  y0 : V.t
  z : V.t
  p0 : SPath s1 x0 y0
  s0 : VSet.t
  s2 : VSet.t
  x : V.t
  y : V.t
  z' : V.t
  H : VSetProp.Add x s0 s2
  H0 : ~ VSet.In x s0
  e : EdgeOf x y
  p : SPath s0 y z'
  hin : VSet.Empty (VSet.inter s2 s')
  q : SPath s' z' z
  inxs' : VSet.In x s'
  H1 : VSet.In x s2 -> x = x \/ VSet.In x s0
  H2 : VSet.In x s2
  ============================
   (VSet.In x s2 /\ VSet.In x s')


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"