theorem
  <*p,PPid(D),p*> is SFHT of D
  proof
    set f = PPid(D);
    for d holds d in dom p & p.d = TRUE & d in dom f & f.d in dom p implies
     p.(f.d) = TRUE;
    then <*p,f,p*> in SFHTs(D);
    hence thesis;
  end;
