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

theorem Th7:
  ( [x,y] in Flow M & x in the carrier' of M implies
  not x in the carrier of M & not y in the carrier' of M &
  y in the carrier of M) &
  ( [x,y] in Flow M & y in the carrier' of M implies
  not y in the carrier of M & not x in the carrier' of M &
  x in the carrier of M) &
  ( [x,y] in Flow M & x in the carrier of M implies
  not y in the carrier of M & not x in the carrier' of M &
  y in the carrier' of M) &
  ( [x,y] in Flow M & y in the carrier of M implies
  not x in the carrier of M & not y in the carrier' of M &
  x in the carrier' of M)
proof
A1: (the carrier of M) misses (the carrier' of M) by NET_1:def 2;
  (Flow M) c= [:the carrier of M, the carrier' of M:] \/ [:the
  carrier' of M, the carrier of M:] by NET_1:def 2;
  hence thesis by A1,SYSREL:7;
end;
