theorem
  <*p,id dom p,p*> is SFHT of D
  proof
    set f = id dom p;
    for d holds d in dom p & p.d = TRUE & d in dom f & f.d in dom p implies
    p.(f.d) = TRUE by FUNCT_1:17;
    then <*p,f,p*> in SFHTs(D);
    hence thesis;
  end;
