Fixpoint DDcut_limit_fix (upcut : DedekindDecCut) (r : Q) (n : nat) :
Qlt 0 r
-> (DDupcut upcut (DDlow upcut + (Z.of_nat n#1) * r))
-> { q : Q | DDupcut upcut q /\ ~DDupcut upcut (q - r) }.

Lemma glb_dec_Q : forall {R : ConstructiveReals} (upcut : DedekindDecCut),
{ x : CRcarrier R
| forall r:Q, (x < CR_of_Q R r -> DDupcut upcut r)
/\ (CR_of_Q R r < x -> ~DDupcut upcut r) }.