let X, Y be set ; G_Net(# (X \/ Y),(id X),(id X) #) is e_net
X c= X \/ Y
by XBOOLE_1:7;
then
( id X c= [:X,X:] & [:X,X:] c= [:(X \/ Y),(X \/ Y):] )
by RELSET_1:13, ZFMISC_1:96;
then A1:
id X c= [:(X \/ Y),(X \/ Y):]
by XBOOLE_1:1;
id X c= (id X) \/ (id Y)
by XBOOLE_1:7;
then
id X c= id (X \/ Y)
by SYSREL:14;
then A2: (id X) * ((id X) \ (id (X \/ Y))) =
(id X) * {}
by XBOOLE_1:37
.=
{}
;
(id X) * (id X) = id X
by SYSREL:12;
hence
G_Net(# (X \/ Y),(id X),(id X) #) is e_net
by A1, A2, Def1, Def2; verum