From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Mon, 14 Jan 2008 15:20:51 +0000 (+0000)
Subject: first lemma
X-Git-Tag: make_still_working~5669
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=acdfb53f9e12dd800bccb3aa2042e33d4bc61fce;p=helm.git

first lemma
---

diff --git a/helm/software/matita/dama/infsup.ma b/helm/software/matita/dama/infsup.ma
new file mode 100644
index 000000000..ef436f889
--- /dev/null
+++ b/helm/software/matita/dama/infsup.ma
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "sandwich_corollary.ma".
+
+(* 3.19 *)
+definition supremum ≝ 
+  λR.λml:mlattice R.λxn:sequence ml.λx:ml.
+    increasing ? xn → upper_bound ? xn x ∧ xn ⇝ x.
+
+definition infimum ≝ 
+  λR.λml:mlattice R.λxn:sequence ml.λx:ml.
+    decreasing ? xn → lower_bound ? xn x ∧ xn ⇝ x.
+    
+(* 3.20 *)
+lemma supremum_uniq:
+  ∀R.∀ml:mlattice R.∀xn:sequence ml.increasing ? xn → (* BUG again the wrong coercion is chosen *)
+   ∀x,y:apart_of_metric_space ? ml.supremum ?? xn x → supremum ?? xn y → x ≈ y.
+intros (R ml xn Hxn x y Sx Sy);
+elim (Sx Hxn) (_ Hx); elim (Sy Hxn) (_ Hy);
+apply (tends_uniq ?? xn ?? Hx Hy);
+qed.
+
+(* 3.21 *)
diff --git a/helm/software/matita/dama/sandwich_corollary.ma b/helm/software/matita/dama/sandwich_corollary.ma
index f41b65028..8dafe1f63 100644
--- a/helm/software/matita/dama/sandwich_corollary.ma
+++ b/helm/software/matita/dama/sandwich_corollary.ma
@@ -42,4 +42,4 @@ change in H with ( δx y/1+ δx y/1< δx y/1+ δx y/1);
 apply (lt_coreflexive ?? H);
 qed.
 
-
+(* 3.18 *)