theorem
  for f being constant Function holds f = (dom f) --> the_value_of f
proof
  let f be constant Function;
  thus dom ((dom f) --> the_value_of f) = dom f;
  let x be object;
  assume
A1: x in dom f;
  then f <> {} & ((dom f) --> the_value_of f).x = the_value_of f by Th7;
  hence thesis by A1,FUNCT_1:def 12;
end;
