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 is_upper_bound_closed :
forall {R : ConstructiveReals}
(E:CRcarrier R -> Prop) (sig_forall_dec : sig_forall_dec_T)
(sig_not_dec : sig_not_dec_T)
(Einhab : exists x : CRcarrier R, E x)
(Ebound : exists x : CRcarrier R, is_upper_bound E x),
is_lub
E (proj1_sig (is_upper_bound_glb
E sig_not_dec sig_forall_dec Einhab Ebound)).