A1:
dom (G .set (WeightSelector,X)) = (dom G) \/ {WeightSelector}
by GLIB_000:7;

WeightSelector in {WeightSelector} by TARSKI:def 1;

then WeightSelector in dom (G .set (WeightSelector,X)) by A1, XBOOLE_0:def 3;

hence not G .set (WeightSelector,X) is plain by GLIB_000:def 5, GLIB_000:1, GLIB_003:def 1, ENUMSET1:def 2; :: thesis: verum

WeightSelector in {WeightSelector} by TARSKI:def 1;

then WeightSelector in dom (G .set (WeightSelector,X)) by A1, XBOOLE_0:def 3;

hence not G .set (WeightSelector,X) is plain by GLIB_000:def 5, GLIB_000:1, GLIB_003:def 1, ENUMSET1:def 2; :: thesis: verum