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

theorem Th1:
  x + y = y implies x = {}
proof
  reconsider o = {} as Element of REAL+ by ARYTM_2:20;
  assume x + y = y;
  then x + y = y + o by ARYTM_2:def 8;
  hence thesis by ARYTM_2:11;
end;
