theorem
  for f being non empty constant Function ex y st for x st x in dom f
  holds f.x = y
proof
  let f be non empty constant Function;
  consider y being object such that
A1: y in rng f by XBOOLE_0:def 1;
  take y;
  ex x0 being object st x0 in dom f & f.x0 = y by A1,FUNCT_1:def 3;
  hence thesis by FUNCT_1:def 10;
end;
