reserve n,m,k for Nat;
reserve x,y,z,X for set;
reserve P,Q for strict chain-complete non empty Poset;
reserve L for non empty Chain of P;
reserve M for non empty Chain of Q;
reserve p,p1,p2,p3,p4 for Element of P;
reserve q,q1,q2 for Element of Q;
reserve f for monotone Function of P,Q;
reserve g,g1,g2 for monotone Function of P,P;

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;
