let I be set ; :: thesis: for M being ManySortedSet of I
for E, T being Element of Bool M holds E (\/) T in Bool M
let M be ManySortedSet of I; :: thesis: for E, T being Element of Bool M holds E (\/) T in Bool M
let E, T be Element of Bool M; :: thesis: E (\/) T in Bool M
( E c= M & T c= M ) by PBOOLE:def 18;
then E (\/) T c= M (\/) M by PBOOLE:20;
then E (\/) T is ManySortedSubset of M by PBOOLE:def 18;
hence E (\/) T in Bool M by Def1; :: thesis: verum