(* The safety property of the system TCG *)

Lemma InvG' :
forall s : S_Ck SG,
match s with
| (sg, z) =>
sg = Open \/
sg = Lowering /\ lt_Ck z kg1 \/
sg = Closed \/ sg = Raising /\ lt_Ck z kg3 ->
InvG s
end.