reconsider a = {} as SubsetFamily of M by XBOOLE_1:2;
let SF be SubsetFamily of M; :: thesis: ( SF is absolutely-multiplicative implies SF is properly-upper-bound )
assume A1: SF is absolutely-multiplicative ; :: thesis: SF is properly-upper-bound
|:a:| = EmptyMS I ;
then A2: meet |:a:| = M by MSSUBFAM:41;
a c= SF ;
hence M in SF by A1, A2; :: according to CLOSURE2:def 8 :: thesis: verum