reserve x,y for object,X,Y for set;
reserve M for Pnet;

theorem
  for X holds the carrier of Pempty_f_net(X) = {} &
  the carrier' of Pempty_f_net(X) = X & Flow Pempty_f_net(X) = {}
proof
  let X;
  {} misses X by XBOOLE_1:65;
  then Pempty_f_net(X) = PT_net_Str (# {}, X, {}({},X), {}(X,{}) #) by Def1;
  hence thesis;
end;
