theorem Th9:
  for g being continuous Function of P,P holds
    least_fix_point(g) = sup iter_min(g)
proof
  let g be continuous Function of P,P;
  set p = sup iter_min(g);
  set q = least_fix_point(g);
  p is_a_fixpoint_of g by Lm8;
  then A1:q <= p by Def5;
  q is_a_fixpoint_of g by Def5;
  then p <= q by Lm9;
  hence thesis by A1,ORDERS_2:2;
end;
