reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem
  X overlaps Z & X c= V implies X overlaps Z (/\) V
proof
  assume that
A1: X overlaps Z and
A2: X c= V;
  consider x such that
A3: x in X and
A4: x in Z by A1,Th11;
  x in V by A2,A3,Th9;
  then x in Z (/\) V by A4,Th8;
  hence thesis by A3,Th10;
end;
