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 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;
