let A be non empty set ; :: thesis: for f being monotone UnOp of (BooleLatt A) ex g being V204() Function of (bool A),(bool A) st lfp (A,g) = lfp f
let f be monotone UnOp of (BooleLatt A); :: thesis: ex g being V204() Function of (bool A),(bool A) st lfp (A,g) = lfp f
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 V204() Function of (bool A),(bool A) by Th49;
reconsider lg = lfp (A,g) as Element of (BooleLatt A) by LATTICE3:def 1;
take g ; :: thesis: lfp (A,g) = lfp f
lg is_a_fixpoint_of f by Th6;
then lfp f [= lg by Th46;
then A1: lf c= lg by LATTICE3:2;
lfp f is_a_fixpoint_of f by Th44;
then lfp (A,g) c= lf by Th10;
hence lfp (A,g) = lfp f by A1, XBOOLE_0:def 10; :: thesis: verum