consider X being non empty finite set , n being Element of NAT , p being FinSeqLen of n, f being Function of (n -tuples_on X),X such that
A1:
S = 1GateCircStr (p,f)
by Def6;
[p,f] in {[p,f]}
by TARSKI:def 1;
then A2:
[p,f] in (rng p) \/ {[p,f]}
by XBOOLE_0:def 3;
the carrier' of S = {[p,f]}
by A1, CIRCCOMB:def 6;
then
union the carrier' of S = [p,f]
by ZFMISC_1:25;
hence
union the carrier' of S is Vertex of S
by A1, A2, CIRCCOMB:def 6; verum