Goal:
    G1 : t  G2 : t  s : VSet.t  x : V.t  y : V.t  p : SPath G2 s x y
  ============================
   (forall (s2 : VSet.t) (x0 z0 : V.t) (s1 : VSet.t) (y0 : V.t),
    DisjointAdd x0 s1 s2 ->
    EdgeOf G2 x0 y0 ->
    forall q : SPath G2 s1 y0 z0,
    (VSet.In y0 (V G1) -> first_in q = y0) ->
    VSet.mem x0 (V G1) = false -> VSet.In x0 (V G1) -> first_in q = x0)


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 ])