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

theorem Th8:
  x <=' y implies x *' z <=' y *' z
proof
  assume x <=' y;
  then consider z0 being Element of REAL+ such that
A1: x + z0 = y by ARYTM_2:9;
  y *' z = x *' z + z0 *' z by A1,ARYTM_2:13;
  hence thesis by ARYTM_2:19;
end;
