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
  a : Z
  lsp1 : Nbar.t
  E0 : to_label (Some a + d)%nbar = Datatypes.S _n_
  h : (Some a + Some w <= lsp1)%nbar
  ============================
   (Z.of_nat (to_label (Some a + d)%nbar) + w <=
    Z.of_nat (to_label (lsp1 + Some (Z.of_nat (k + l x)))%nbar))


DEBUG:Going to execute:
case not_locked_false_eq_true; Ltac.assumption
Level 1: Backtrace:

Not an inductive goal with 1 constructor.
Level 0: Backtrace:

Not an inductive goal with 1 constructor.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.