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

theorem Th12:
  CL the entrance of N = CL the escape of N
proof
  (the escape of N) * ((the escape of N) \ id N) = {} by Def2; then
A1: (the escape of N) * ((the escape of N) \ id dom the escape of N) = {}
  by Th11;
  (the entrance of N) * ((the entrance of N) \ id N) = {} by Def2; then
A2: (the entrance of N) * ((the entrance of N) \ id dom the entrance of N
  ) = {} by Th11;
  (the entrance of N) * (the escape of N) = the entrance of N &
  (the escape of N) * (the entrance of N) = the escape of N by Def1;
  hence thesis by A1,A2,SYSREL:40;
end;
