Definition InvTick (s : StGlobal) :=
  match s with
  | ((st, x), ((sc, y), (sg, z))) =>
      (fun s : StGlobal =>
       match s with
       | (st_x, (sc_y, sg_z)) => InvT st_x /\ InvC sc_y /\ InvG sg_z
       end) (st, Inc x, (sc, Inc y, (sg, Inc z)))
  end.Definition noInvTick (s : StGlobal) :=
  match s with
  | ((st, x), ((sc, y), (sg, z))) =>
      ~ InvTick (st, x, (sc, y, (sg, z))) ->
      RState TrGlobal SiniTCG (st, x, (sc, y, (sg, z))) ->
      (st = Near /\ gt_Ck x kt1 \/ st = Inside) \/
      InvT (st, Inc x) /\ (sc = Sc2 /\ eq_Ck y kc1 \/ sc = Sc4) \/
      InvT (st, Inc x) /\
      InvC (sc, Inc y) /\ (sg = Lowering \/ sg = Raising /\ ge_Ck z kg2)
  end.

Lemma NoInvTick : forall s : StGlobal, noInvTick s.