consider EqR being Equivalence_Relation of A such that

A1: D = Class EqR by EQREL_1:34;

A1: D = Class EqR by EQREL_1:34;

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

end;

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;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