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

theorem Th10:
  G_Net (# X \/ Y, id X, id X #) is e_net
proof
  X c= X \/ Y by XBOOLE_1:7;
  then id(X) c= [:X, X:] & [:X, X:] c= [:X \/ Y, X \/ Y:] by RELSET_1:13
,ZFMISC_1:96; then
A1: id(X) c= [:X \/ Y, X \/ Y:] by XBOOLE_1:1;
  id(X) c= id(X) \/ id(Y) by XBOOLE_1:7;
  then id(X) c= id(X \/ Y) by SYSREL:14; then
A2: id(X) * (id(X) \ id(X \/ Y)) = id(X) * {} by XBOOLE_1:37
    .= {};
  id(X) * id(X) = id(X) by SYSREL:12;
  hence thesis by A1,A2,Def1,Def2;
end;
