let I be set ; :: thesis: for M being ManySortedSet of I
for SF, SG being MSSubsetFamily of M holds SF \/ SG is MSSubsetFamily of M
let M be ManySortedSet of I; :: thesis: for SF, SG being MSSubsetFamily of M holds SF \/ SG is MSSubsetFamily of M
let SF, SG be MSSubsetFamily of M; :: thesis: SF \/ SG is MSSubsetFamily of M
SF \/ SG is ManySortedSubset of bool M

proof

A1: SF c= bool M by PBOOLE:def 23;
SG c= bool M by PBOOLE:def 23;
hence SF \/ SG c= bool M by A1, PBOOLE:18; :: according to PBOOLE:def 23 :: thesis: verum

end;

hence SF \/ SG is MSSubsetFamily of M ; :: thesis: verum