(* 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_Inv3 : ForAll TrGlobal SiniTCG Inv3.
Definition Inv4 (s : StGlobal) :=
match s with
| ((st, _), ((sc, _), _)) => st = Near -> sc = Sc2 \/ sc = Sc3
end.