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