theorem
  CnIPC(CnIPC(X)) = CnIPC(X)
proof
A1: CnIPC(X) c= CnIPC(CnIPC(X)) by Th12;
  CnIPC(CnIPC(X)) c= CnIPC(X) by Lm2;
  hence thesis by A1,XBOOLE_0:def 10;
end;
