reserve x,y for object,X,Y for set;
reserve M for Pnet;

theorem Th8:
  (Flow M) c= [:Elements(M), Elements(M):] &
  (Flow M)~ c= [:Elements(M), Elements(M):]
proof
A1: the carrier of M c= Elements(M) by XBOOLE_1:7;
A2: the carrier' of M c= Elements(M) by XBOOLE_1:7;
  then
A3: [:the carrier of M, the carrier' of M:] c=
  [:Elements(M), Elements(M):] by A1,ZFMISC_1:96;
  [:the carrier' of M, the carrier of M:] c=
  [:Elements(M), Elements(M):] by A1,A2,ZFMISC_1:96;
  then
A4: [:the carrier of M, the carrier' of M:] \/
  [:the carrier' of M, the carrier of M:] c=
  [:Elements(M), Elements(M):] by A3,XBOOLE_1:8;
  Flow M c= [:the carrier of M, the carrier' of M:] \/
  [:the carrier' of M, the carrier of M:] by NET_1:def 2;
  then (Flow M) c= [:Elements(M), Elements(M):] by A4,XBOOLE_1:1;
  hence thesis by SYSREL:4;
end;
