A3:
dom (G .set (VLabelSelector,X)) = (dom G) \/ {VLabelSelector}
by GLIB_000:7;
VLabelSelector in {VLabelSelector}
by TARSKI:def 1;
then
VLabelSelector in dom (G .set (VLabelSelector,X))
by A3, XBOOLE_0:def 3;
hence
not G .set (VLabelSelector,X) is plain
by GLIB_000:def 5, GLIB_000:1, GLIB_003:def 3, ENUMSET1:def 2; verum