let N be e_net; :: thesis: ( 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) )

( 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 ( 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) ) by SYSREL:20; :: thesis: verum

( 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 ( 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) ) by SYSREL:20; :: thesis: verum