Stuff moved from old Matita.

[helm.git] / matita / matita / library / dama / models / nat_lebesgue.ma

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+  (**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "dama/lebesgue.ma".
+include "dama/models/nat_order_continuous.ma".
+
+alias symbol "dependent_pair" = "dependent pair".
+theorem nat_lebesgue_oc:
+   ∀a:sequence ℕ.∀s:‡ℕ.∀H:∀i:nat.a i ∈ s. 
+     ∀x:ℕ.a order_converges x → 
+      x ∈ s ∧ 
+      ∀h:x ∈ s.
+       uniform_converge {[s]} ⌊n,≪a n,H n≫⌋ ≪x,h≫.
+intros; apply lebesgue_oc; [apply nat_us_is_oc] assumption;
+qed.
+