Goal:
  
  G : t
  invG : invariants G
  acG : acyclic_no_loop G
  l : labelling
  Hl : correct_labelling G l
  x : V.t
  k : nat
  d := Some (Z.of_nat (k + l x)) : option Z
  Hk : (lsp G x (s G) + d <= Some 0)%nbar
  Hl0 : l (s G) = 0%nat
  Hledge : forall e : EdgeSet.elt,
           EdgeSet.In e (E G) ->
           Z.of_nat (l e..s) + e..w <= Z.of_nat (l e..t)
  s : V.t
  w : Z
  t : V.t
  he : EdgeSet.In (s, w, t) (E G)
  u := to_label (lsp G x (s, w, t)..s + d)%nbar : nat
  hs : VSet.In (s, w, t)..s (V G)
  ht : VSet.In (s, w, t)..t (V G)
  E : to_label (lsp G x s + d)%nbar = 0%nat
  ============================
   (Z.of_nat (l s) + w <= Z.of_nat (l t) ->
    (lsp G x s + Some w <= lsp G x t)%nbar ->
    (l s <= 0)%nat ->
    Z.of_nat 0 + w <=
    Z.of_nat
      (Nat.max (l t) (to_label (lsp G x t + Some (Z.of_nat (k + l x)))%nbar)))


DEBUG:Going to execute:
etransitivity ; last  apply : inj_le ; apply : Nat.le_max_l 
DEBUG LTAC Evaluated term: (to_label ?z)