Goal:
  
  G1 : t
  G2 : t
  H : invariants G1
  ext := EdgeSet.diff (E G2) (E G1) : EdgeSet.t
  bs := border_set G1 ext : VSet.t
  s : VSet.t
  x : V.t
  y : V.t
  z : V.t
  eo : EdgeOf G2 x y
  p : SPath G2 s y z
  e := (x, eo.π1, y) : (V.t × Z) × V.t
  hx : VSet.In x (V G1)
  hz : VSet.In z (V G1)
  heo : ~ EdgeSet.In e (E G1)
  he : EdgeSet.In e ext
  ============================
   (VSet.In x (V G1))


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | Ltac.split ]
            | case not_locked_false_eq_true; Ltac.assumption
            | match goal with
              | H:~ _ |- _ => solve [ case H; trivial ]
              end ])