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

theorem
  x *' y = {} implies x = {} or y = {}
proof
  assume
A1: x *' y = {};
  assume x <> {};
  then consider x1 being Element of REAL+ such that
A2: x *' x1 = one by ARYTM_2:14;
  thus y = x *' x1 *' y by A2,ARYTM_2:15
    .= x *' y *' x1 by ARYTM_2:12
    .= {} by A1,ARYTM_2:4;
end;
