
theorem Th18:
  for A being Universal_Algebra, B being Subset of A holds B|^0 = B
proof
  let A be Universal_Algebra;
  let B be Subset of A;
  ex F being sequence of  bool the carrier of A st B|^0 = F.0 & F.0 = B &
  for n being Nat holds F.(n+1) = F.n \/ {Den(o,A).p where o is (Element of
  dom the charact of A), p is Element of (the carrier of A)*: p in dom
  Den(o,A) & rng p c= F.n} by Def8;
  hence thesis;
end;
