(* Some invariants of the system TCG *)
Definition Inv1 (s : StGlobal) :=
match s with
| ((st, _), ((sc, _), (sg, _))) =>
st = Near \/ st = Inside -> sc = Sc3 -> sg = Closed \/ sg = Lowering
end.

Lemma lema_Inv7 : ForAll TrGlobal SiniTCG Inv7.
Definition Inv8 (s : StGlobal) :=
match s with
| ((st, x), ((sc, _), (sg, _))) =>
st = Near /\ gt_Ck x kt1 \/ st = Inside -> sg = Closed
end.