theorem Th11:
  dom (f^^) = dom (f|(dom (f^)))
proof
A1: dom (f^) = dom f \ f"{0c} by Def2;
  thus dom (f^^) = dom (f^) \(f^)"{0c} by Def2
    .= dom (f^) \ {} by Th9
    .= dom f /\ dom (f^) by A1,XBOOLE_1:28,36
    .= dom (f|(dom (f^))) by RELAT_1:61;
end;
