reserve X for set;
reserve UN for Universe;

theorem Th88:
  for X being set
  ex f being Function st dom f = NAT & f.0 = X &
  for n being Nat holds f.(n+1) = GrothendieckUniverse (f.n)
  proof
    let X be set;
    deffunc G(set,set) = GrothendieckUniverse $2;
    ex f be Function st dom f = NAT & f.0 = X & for n be Nat holds
      f.(n+1) = G(n,f.n) from NAT_1:sch 11;
    hence thesis;
  end;
