Goal:
  
  G : t
  invG : invariants G
  acG : acyclic_no_loop G
  x : V.t
  y : V.t
  hx : VSet.In x (V G)
  hy : VSet.In y (V G)
  nxy : Z
  hxy : (lsp G x y <= Some nxy)%nbar
  nx : Z
  eqlspx : lsp G (s G) x = Some nx
  nxpos : 0 <= nx
  eqnx : Z.of_nat (to_label (lsp G (s G) x)) = nx
  ny : Z
  eqlspy : lsp G (s G) y = Some ny
  nypos : 0 <= ny
  eqny : Z.of_nat (to_label (lsp G (s G) y)) = ny
  _a_ : Z
  E : lsp G x (s G) = Some _a_
  ============================
   ((None <= Some nxy)%nbar ->
    (Some _a_ + Some ny <= None)%nbar ->
    (Some nx + Some _a_ <= Some 0)%nbar ->
    (Some _a_ + Some (Z.max 0 (ny - nx - nxy)) + Some nx <= Some 0)%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 ])