
theorem Th44:
  for x,y,z being object holds (x .--> y) +* (x,z) = x .--> z
proof
  let x,y,z be object;
  dom (x .--> y) = dom ({x} --> y) by FUNCOP_1:def 9
    .= {x};
  then x in dom (x .--> y) by TARSKI:def 1;
  then (x .--> y) +* (x,z) = (x .--> y) +* (x .--> z) by FUNCT_7:def 3;
  hence thesis by Th12;
end;
