theorem Th10:
  for g1,g2 being continuous Function of P,P st g1 <= g2 holds
    least_fix_point(g1) <= least_fix_point(g2)
proof
  let g1,g2 be continuous Function of P,P;
  assume A1: g1 <= g2;
  set p1 = sup iter_min(g1);
  set p2 = sup iter_min(g2);
  p1 = least_fix_point(g1) & p2 = least_fix_point(g2) by Th9;
  hence thesis by A1,Th5;
end;
