consider R being Relation such that
A1: R = {} ;
set f = I --> R;
reconsider f = I --> R as ManySortedSet of I ;
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) )
f . i = {} by A1;
hence ( i in I implies f . i is Relation of (A . i),(B . i) ) by RELSET_1:12; :: thesis: verum

end;

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