let N be e_net; :: thesis: ( e_prox N c= [:(e_shore N),(e_shore N):] & e_flow N c= [:(e_shore N),(e_shore N):] )

A1: id the carrier of N c= [: the carrier of N, the carrier of N:] by RELSET_1:13;

A2: the escape of N c= [: the carrier of N, the carrier of N:] by Def1;

A3: the entrance of N c= [: the carrier of N, the carrier of N:] by Def1;

then the entrance of N ~ c= [: the carrier of N, the carrier of N:] by SYSREL:4;

then A4: ( the entrance of N ~) \/ the escape of N c= [: the carrier of N, the carrier of N:] by A2, XBOOLE_1:8;

the entrance of N \/ the escape of N c= [: the carrier of N, the carrier of N:] by A3, A2, XBOOLE_1:8;

hence ( e_prox N c= [:(e_shore N),(e_shore N):] & e_flow N c= [:(e_shore N),(e_shore N):] ) by A4, A1, SYSREL:4, XBOOLE_1:8; :: thesis: verum

A1: id the carrier of N c= [: the carrier of N, the carrier of N:] by RELSET_1:13;

A2: the escape of N c= [: the carrier of N, the carrier of N:] by Def1;

A3: the entrance of N c= [: the carrier of N, the carrier of N:] by Def1;

then the entrance of N ~ c= [: the carrier of N, the carrier of N:] by SYSREL:4;

then A4: ( the entrance of N ~) \/ the escape of N c= [: the carrier of N, the carrier of N:] by A2, XBOOLE_1:8;

the entrance of N \/ the escape of N c= [: the carrier of N, the carrier of N:] by A3, A2, XBOOLE_1:8;

hence ( e_prox N c= [:(e_shore N),(e_shore N):] & e_flow N c= [:(e_shore N),(e_shore N):] ) by A4, A1, SYSREL:4, XBOOLE_1:8; :: thesis: verum