general reorganization and first (unconditional) proof of lebesgue over naturals

[helm.git] / helm / software / matita / contribs / dama / dama / models / nat_lebesgue.ma

diff --git a/helm/software/matita/contribs/dama/dama/models/nat_lebesgue.ma b/helm/software/matita/contribs/dama/dama/models/nat_lebesgue.ma
new file mode 100644 (file)
index 0000000..228392d
--- /dev/null
+++ b/helm/software/matita/contribs/dama/dama/models/nat_lebesgue.ma
@@ -0,0 +1,27 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "lebesgue.ma".
+include "models/nat_order_continuous.ma".
+
+alias symbol "pair" = "dependent pair".
+theorem nat_lebesgue_oc:
+   ∀a:sequence ℕ.∀l,u:nat_ordered_uniform_space.∀H:∀i:nat.a i ∈ [l,u]. 
+     ∀x:ℕ.a order_converges x → 
+      x ∈ [l,u] ∧ 
+      ∀h:x ∈ [l,u].
+       uniform_converge {[l,u]} (⌊n,〈a n,H n〉⌋) 〈x,h〉.
+intros; apply lebesgue_oc; [apply nat_us_is_oc] assumption;
+qed.
+