theorem
  {x,y} \/ Z c= Z implies x in Z
proof
  assume
A1: {x,y} \/ Z c= Z;
  assume not x in Z;
  then not x in {x,y} \/ Z by A1;
  then not x in {x,y} by XBOOLE_0:def 3;
  hence thesis by TARSKI:def 2;
end;
