Goal:
  
  G1 : t
  G2 : t
  on_edge : forall x y : V.t, EdgeOf G1 x y -> EdgeOf G2 x y
  weight_on_edge : forall (x y : V.t) (e : EdgeOf G1 x y),
                   (on_edge x y e).π1 <= e.π1
  s : VSet.t
  x : V.t
  y : V.t
  p : SPath G1 s x y
  ============================
   (forall (s : VSet.t) (x y : V.t) (s1 : VSet.t) (y' : V.t),
    DisjointAdd x s1 s ->
    forall (e : EdgeOf G1 x y') (p : SPath G1 s1 y' y),
    sweight (map_spath p) <= sweight p ->
    (on_edge x y' e).π1 + sweight (map_spath p) <= e.π1 + sweight p)


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 ])