proposition: Lemma limsup_decr : forall f:natO-m>UI, limsup f == glb f.
proof: Proof. unfold limsup;intros. apply glb_eq_compat; apply fmon_eq_intro; simpl; unfold fsup; intro. apply (Oeq_trans (O:=UI)) with (Ulub (mseq_lift_left f n)); auto. apply (Oeq_trans (O:=UI)) with (mseq_lift_left f n O); auto. apply Uopp_eq; apply (Ulub_mon (mseq_lift_left f n)). simpl; replace (n+0)%nat with n; auto with arith. Qed.
imports: ALEA(Utheory)