let I be set ; :: thesis: for X, Y, Z being ManySortedSet of I st X overlaps Y & Y c= Z holds
X overlaps Z
let X, Y, Z be ManySortedSet of I; :: thesis: ( X overlaps Y & Y c= Z implies X overlaps Z )
assume that
A1: X overlaps Y and
A2: Y c= Z ; :: thesis: X overlaps Z
consider x being ManySortedSet of I such that
A3: x in X and
A4: x in Y by A1, Th11;
x in Z by A2, A4, Th9;
hence X overlaps Z by A3, Th10; :: thesis: verum