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
  k : nat
  _p_ : positive
  ============================
   (0 <= Z.pos _p_ ->
    (Pos.to_nat _p_ + k)%nat =
    match
      match Z.of_nat k with
      | 0 => Z.pos _p_
      | Z.pos y' => Z.pos (_p_ + y')
      | Z.neg y' => Z.pos_sub _p_ y'
      end
    with
    | Z.pos p => Pos.to_nat p
    | _ => 0%nat
    end)


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 ])