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

theorem
  (f_escape(M)) * (f_escape(M) \ id(Elements(M))) = {} &
  (f_entrance(M)) * (f_entrance(M) \ id(Elements(M))) = {}
proof
  set R = (Flow M)|(the carrier of M);
  set S = id(the carrier' of M);
A1: S * R = {} by Th12;
  (f_escape(M)) * (f_escape(M) \ id(Elements(M))) = (R \/ S) * R by Th14
    .= (R * R) \/ (S * R) by SYSREL:6
    .= {} by A1,Th11;
  hence (f_escape(M)) * (f_escape(M) \ id(Elements(M))) = {};
  set R = ((Flow M)~|(the carrier of M));
A2: S * R = {} by Th12;
  (f_entrance(M)) * (f_entrance(M) \ id(Elements(M))) = (R \/ S) * R by Th14
    .= (R * R) \/ (S * R) by SYSREL:6
    .= {} by A2,Th11;
  hence thesis;
end;
