theorem
  ex g being c=-monotone Function of bool A, bool A st lfp (A, g) = lfp f
proof
  reconsider lf = lfp f as Subset of A by LATTICE3:def 1;
  the carrier of BooleLatt A = bool A by LATTICE3:def 1;
  then reconsider g = f as c=-monotone Function of bool A, bool A by Th46;
  reconsider lg = lfp(A, g) as Element of BooleLatt A by LATTICE3:def 1;
  take g;
  lg is_a_fixpoint_of f by Th4;
  then lfp f [= lg by Th43;
  then
A1: lf c= lg by LATTICE3:2;
  lfp f is_a_fixpoint_of f by Th41;
  then lfp (A, g) c= lf by Th8;
  hence thesis by A1;
end;
