reserve x,y,z for object,X,Y for set;
reserve N for e_net;

theorem Th11:
  (the entrance of N) \ id(dom(the entrance of N)) =
    (the entrance of N) \ id the carrier of N &
  (the escape of N) \ id(dom(the escape of N)) =
    (the escape of N) \ id the carrier of N &
  (the entrance of N) \ id(rng(the entrance of N)) =
    (the entrance of N) \ id the carrier of N &
  (the escape of N) \ id(rng(the escape of N)) =
    (the escape of N) \ id the carrier of N
proof
  the entrance of N c= [:the carrier of N,the carrier of N:] & the escape
  of N c= [:the carrier of N,the carrier of N:] by Def1;
  hence thesis by SYSREL:20;
end;
