theorem
  for f being Function holds [:{},f:] = {} & [:f,{}:] = {}
proof
  let f be Function;
  dom [:{},f:] = [:dom {},dom f:] & dom [:f,{}:] = [:dom f,dom {}:] by
FUNCT_3:def 8;
  hence thesis by ZFMISC_1:90;
end;
