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)
  _n_ : nat
  Hledge0 : Z.of_nat (l s) + w <= Z.of_nat (l t)
  ule : (l s <= Datatypes.S _n_)%nat
  ============================
   (forall (a : Z) (lsp : Nbar.t),
    to_label (Some a + d)%nbar = Datatypes.S _n_ ->
    (Some a + Some w <= lsp)%nbar ->
    Z.of_nat (to_label (Some a + d)%nbar) + w <=
    Z.of_nat (to_label (lsp + Some (Z.of_nat (k + l x)))%nbar))


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 ])