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

theorem Th25:
  ((the escape of N) \ id(the carrier of N))~ *
    ((the escape of N) \ id(the carrier of N))~ = {} &
  ((the entrance of N) \ id(the carrier of N))~ *
    ((the entrance of N) \ id(the carrier of N))~ = {}
proof
A1: ((the entrance of N) \ id(the carrier of N))~ * ((the entrance of N) \
id(the carrier of N))~ = (((the entrance of N) \ id(the carrier of N)) * ((the
  entrance of N) \ id(the carrier of N)))~ by RELAT_1:35
    .= {} by Th24,RELAT_1:43;
  ((the escape of N) \ id(the carrier of N))~ * ((the escape of N) \ id(
  the carrier of N))~ = (((the escape of N) \ id(the carrier of N)) * ((the
  escape of N) \ id(the carrier of N)))~ by RELAT_1:35
    .= {} by Th24,RELAT_1:43;
  hence thesis by A1;
end;
