(* 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_Inv2 : ForAll TrGlobal SiniTCG Inv2.
Definition Inv3 (s : StGlobal) :=
match s with
| ((st, x), ((_, y), _)) => st = Near \/ st = Inside -> eq_Ck x y
end.