reserve x,y,z for Element of REAL+;

theorem Th9:
  x <=' y or x -' y <> {}
proof
  assume
A1: not x <=' y;
  assume
A2: x -' y = {};
  x -' y + y = x by A1,Def1;
  then x = y by A2,ARYTM_2:def 8;
  hence contradiction by A1;
end;
