let I be set ; :: thesis: for X, Y, Z being ManySortedSet of I st X overlaps Y (/\) Z holds
( X overlaps Y & X overlaps Z )
let X, Y, Z be ManySortedSet of I; :: thesis: ( X overlaps Y (/\) Z implies ( X overlaps Y & X overlaps Z ) )
assume X overlaps Y (/\) Z ; :: thesis: ( X overlaps Y & X overlaps Z )
then consider x being ManySortedSet of I such that
A1: x in X and
A2: x in Y (/\) Z by Th11;
( x in Y & x in Z ) by A2, Th8;
hence ( X overlaps Y & X overlaps Z ) by A1, Th10; :: thesis: verum