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

theorem Th28:
  id((the carrier of N) \ rng(the escape of N)) *
    ((the escape of N) \ id(the carrier of N))~ = {} &
  id((the carrier of N) \ rng(the entrance of N)) *
    ((the entrance of N) \ id(the carrier of N))~ = {}
proof
A1: id((the carrier of N) \ rng(the entrance of N)) * ((the entrance of N) \
id(the carrier of N))~ = (id((the carrier of N) \ rng(the entrance of N)))~ * (
  (the entrance of N) \ id(the carrier of N))~
    .= (((the entrance of N) \ id(the carrier of N)) * (id((the carrier of N
  ) \ rng(the entrance of N))))~ by RELAT_1:35
    .= {} by Th27,RELAT_1:43;
  id((the carrier of N) \ rng(the escape of N)) * ((the escape of N) \ id(
the carrier of N))~ = (id((the carrier of N) \ rng(the escape of N)))~ * ((the
  escape of N) \ id(the carrier of N))~
    .= (((the escape of N) \ id(the carrier of N)) * (id((the carrier of N)
  \ rng(the escape of N))))~ by RELAT_1:35
    .= {} by Th27,RELAT_1:43;
  hence thesis by A1;
end;
