consider EqR being Equivalence_Relation of A such that
A1: D = Class EqR by EQREL_1:34;

per cases ( not D is empty or D is empty ) ;

suppose not D is empty ; :: thesis: (support f) /\ X is Subset of A

then X in Class EqR by A1;
then consider x being object such that
x in A and
A2: X = Class (EqR,x) by EQREL_1:def 3;
thus (support f) /\ X is Subset of A by A2, XBOOLE_1:108; :: thesis: verum

end;

suppose D is empty ; :: thesis: (support f) /\ X is Subset of A

then X = {} by SUBSET_1:def 1;
hence (support f) /\ X is Subset of A by XBOOLE_1:2; :: thesis: verum

end;

end;