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

theorem
  for R, S being Relation holds G_Net (# X, R, S #) is e_net iff
  R c= [:X,X:] & S c= [:X,X:] & R * R = R & R * S = R &
  S * S = S & S * R = S & R * (R \ id X) = {} & S * (S \ id X) = {}
    by Def1,Def2;
