let A be non empty set ; :: thesis: for f being monotone UnOp of (BooleLatt A) ex g being V202() Function of (bool A),(bool A) st gfp A,g = gfp f
let f be monotone UnOp of (BooleLatt A); :: thesis: ex g being V202() Function of (bool A),(bool A) st gfp A,g = gfp f
the carrier of (BooleLatt A) = bool A by LATTICE3:def 1;
then reconsider g = f as V202() Function of (bool A),(bool A) by Th49;
take g ; :: thesis: gfp A,g = gfp f
reconsider gf = gfp f as Subset of A by LATTICE3:def 1;
gfp f is_a_fixpoint_of f by Th45;
then A1: gf c= gfp A,g by Th10;
reconsider gg = gfp A,g as Element of (BooleLatt A) by LATTICE3:def 1;
gg is_a_fixpoint_of f by Th7;
then gg [= gfp f by Th46;
then gg c= gf by LATTICE3:2;
hence gfp A,g = gfp f by A1, XBOOLE_0:def 10; :: thesis: verum