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

theorem
  G_Net (# X, id(X \ Y), id(X \ Y) #) is e_net
proof
A1: id(X \ Y) * (id(X \ Y) \ id X) = id(X \ Y) * {} by SYSREL:16
    .= {};
  X \ Y c= X by XBOOLE_1:36; then
A2: [:X \ Y, X \ Y:] c= [:X, X:] by ZFMISC_1:96;
  id(X \ Y) c= [:X \ Y, X \ Y:] by RELSET_1:13; then
A3: id(X \ Y) c= [:X, X:] by A2,XBOOLE_1:1;
  id(X \ Y) * id(X \ Y) = id(X \ Y) by SYSREL:12;
  hence thesis by A3,A1,Def1,Def2;
end;
