theorem
  I <= J & J <= I implies I = J
 proof assume CutLastLoc I c= J;
  then
A1: CutLastLoc I c= CutLastLoc J by Th18;
  assume CutLastLoc J c= I;
   then CutLastLoc J c= CutLastLoc I by Th18;
   then  CutLastLoc I = CutLastLoc J by A1,XBOOLE_0:def 10;
  hence I = J by Th21;
 end;
