Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  y_0 : V.t
  x_0 : V.t
  Vx : VSet.In x_0 (V G)
  Vy : VSet.In y_0 (V G)
  K : Z
  Hxs : lsp G x_0 y_0 = Some K
  XX : correct_labelling G' (fun x : V.t => to_label (lsp G' (s G') x))
  ============================
   (forall e : EdgeSet.elt,
    EdgeSet.In e (E G) ->
    Z.of_nat (to_label (lsp G' (s G') e..s)) + e..w <=
    Z.of_nat (to_label (lsp G' (s G') e..t)))


DEBUG:Going to execute:
intros e He; apply XX