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) }.