reserve X for set;
reserve UN for Universe;

theorem Th53:
  for UN being non trivial Universe holds REAL is Element of UN
  proof
    let UN be non trivial Universe;
    reconsider n = NAT as Element of UN by Def6;
    reconsider n1 = [:n,n:] \/ n as Element of UN;
    reconsider n2 = n1 \/ bool n1 as Element of UN;
    REAL c= n2 \/ [:n,n2:] by Th52;
    hence thesis by Th13;
  end;
