theorem
  f = 1(#)f
proof
A1: dom f = dom (1(#)f) by MESFUNC1:def 6;
 for x st x in dom (1(#)f) holds f.x = (1(#)f).x
  proof
    let x;
    assume x in dom(1(#)f);
then  (1(#)f).x = (1) * f.x by MESFUNC1:def 6;
    hence thesis by XXREAL_3:81;
  end;
  hence thesis by A1,PARTFUN1:5;
end;
