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 c= bool M & SG c= bool M ) by PBOOLE:def 23;
then SF \/ SG c= bool M by PBOOLE:18;
hence SF \/ SG is MSSubsetFamily of M by PBOOLE:def 23; :: thesis: verum