helm/software/matita/library/dama/models/nat_lebesgue.ma

   1   (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "lebesgue.ma".
  16 include "models/nat_order_continuous.ma".
  17
  18 theorem nat_lebesgue_oc:
  19    ∀a:sequence ℕ.∀s:‡ℕ.∀H:∀i:nat.a i ∈ s.
  20      ∀x:ℕ.a order_converges x →
  21       x ∈ s ∧
  22       ∀h:x ∈ s.
  23        uniform_converge {[s]} ⌊n,≪a n,H n≫⌋ ≪x,h≫.
  24 intros; apply lebesgue_oc; [apply nat_us_is_oc] assumption;
  25 qed.
  26