theorem
  for f be Function,d,r be set st d in dom f holds dom f=dom (f+*(d.-->r
  ))
proof
  let f be Function,d,r be set;
  assume
A1: d in dom f;
  thus dom f=dom (f+*(d,r)) by Th29
    .=dom (f+*(d.-->r)) by A1,Def2;
end;
