
theorem Th12:
  for x,y,z being object holds (x .--> y) +* (x .--> z) = x .--> z
proof
  let x,y,z be object;
  A1: dom (x .--> y) = dom ({x} --> y) by FUNCOP_1:def 9
    .= {x};
  dom (x .--> z) = dom ({x} --> z) by FUNCOP_1:def 9
    .= {x};
  hence thesis by A1, FUNCT_4:19;
end;
