Goal:
  
  G : t
  x : V.t
  y : V.t
  s : VSet.t
  s' : VSet.t
  p : SPath G s x y
  q : SPath G s' y x
  acG : acyclic_no_loop G
  ============================
   (weight (to_pathOf G p) <= - weight (to_pathOf G q) ->
    weight (to_pathOf G p) <= - weight (to_pathOf G q))


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 ])