consider R being Relation such that
A1: R = {} ;
set f = I --> R;
dom (I --> R) = I by FUNCOP_1:19;
then reconsider f = I --> R as ManySortedSet of I by PARTFUN1:def 4;
take f ; :: thesis: for i being set st i in I holds
f . i is Relation of (A . i),(B . i)
for i being set st i in I holds
f . i is Relation of (A . i),(B . i)

proof

let i be set ; :: thesis: ( i in I implies f . i is Relation of (A . i),(B . i) )
assume i in I ; :: thesis: f . i is Relation of (A . i),(B . i)
then f . i = {} by A1, FUNCOP_1:13;
hence f . i is Relation of (A . i),(B . i) by RELSET_1:25; :: thesis: verum

end;

hence for i being set st i in I holds
f . i is Relation of (A . i),(B . i) ; :: thesis: verum