From d80bd0bc5253538759bfb13c98e86d07592a9359 Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Thu, 8 Nov 2007 17:03:23 +0000
Subject: [PATCH] xxx

---
 .../dama/constructive_pointfree/lebesgue.ma   | 75 +++++++++++++++++++
 1 file changed, 75 insertions(+)
 create mode 100644 matita/dama/constructive_pointfree/lebesgue.ma

diff --git a/matita/dama/constructive_pointfree/lebesgue.ma b/matita/dama/constructive_pointfree/lebesgue.ma
new file mode 100644
index 000000000..583dc638c
--- /dev/null
+++ b/matita/dama/constructive_pointfree/lebesgue.ma
@@ -0,0 +1,75 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/lebesgue/".
+
+include "reals.ma".
+include "lattices.ma".
+
+record measured_set (R : real) : Type ≝ {
+  ms_carr :> Type;
+  ms_measure: ms_carr → ms_carr → R
+}.
+
+notation "\delta" non associative with precedence 90 for @{ 'delta }.
+interpretation "measure" 'delta = (cic:/matita/lebesgue/ms_measure.con _ _).
+
+record pre_measured_lattice (R : real) : Type ≝ {
+  ml_lattice :> lattice;
+  ml_measured_set_ : measured_set R;
+  with_ml_lattice_eq_ml_measured_set_: ms_carr ? ml_measured_set_ = ml_lattice
+}.
+
+lemma ml_measured_set : ∀R.∀ms:pre_measured_lattice R. measured_set R.
+intros (R ml); constructor 1; [1:apply (ml : Type);] cases ml; 
+rewrite < H; clear H; cases ml_measured_set_; simplify; exact f;
+qed.  
+
+coercion cic:/matita/lebesgue/ml_measured_set.con.
+
+record is_measured_lattice (R : real) (ml : pre_measured_lattice R) : Prop ≝ {
+  prop1a: ∀a : ml.δ (a ∧ a) a = 0;
+  prop1b: ∀a : ml.δ (a ∨ a) a = 0;
+  prop2a: ∀a,b: ml. δ (a ∨ b) (b ∨ a) = 0;
+  prop2b: ∀a,b: ml. δ (a ∧ b) (b ∧ a) = 0;
+  prop3a: ∀a,b,c: ml. δ (a ∨ (b ∨ c)) ((a ∨ b) ∨ c) = 0;
+  prop3b: ∀a,b,c: ml. δ (a ∧ (b ∧ c)) ((a ∧ b) ∧ c) = 0;
+  prop4a: ∀a,b: ml. δ (a ∨ (a ∧ b)) a = 0;
+  prop4b: ∀a,b: ml. δ (a ∧ (a ∨ b)) a = 0;
+  prop5: ∀a,b,c: ml. δ (a ∨ b) (a ∨ c) + δ (a ∧ b) (a ∧ c) ≤ δ b c
+}. 
+  
+record measured_lattice (R : real) : Type ≝ {
+  ml_pre_measured_lattice:> pre_measured_lattice R;
+  ml_measured_lattice_properties: is_measured_lattice R ml_pre_measured_lattice
+}.
+  
+definition apart:= 
+ λR: real. λml: measured_lattice R. λa,b: ml. 0 < δ a b.
+ (* < scazzato, ma CSC dice che poi si cambia dopo  *)    
+
+notation "a # b" non associative with precedence 50 for
+ @{ 'apart $a $b}.
+interpretation "measured lattice apartness" 'apart a b =
+ (cic:/matita/lebesgue/apart.con _ _ a b). 
+notation "a \approx b" non associative with precedence 50 for
+ @{ 'napart $a $b}.
+interpretation "measured lattice non apartness" 'napart a b =
+ (cic:/matita/logic/connectives/Not.con
+   (cic:/matita/lebesgue/apart.con _ _ a b)). 
+
+lemma foo : ∀R: real. ∀ml: measured_lattice R.∀a,b,a1,b1: ml. 
+  a ≈ a1 → b ≈ b1 → δ a b = δ a1 b1. 
+     (* =R scazzato *)  
+intros;
-- 
2.39.2