bir georganization, most of the structures done

[helm.git] / helm / software / matita / dama / constructive_pointfree / lebesgue.ma

diff --git a/helm/software/matita/dama/constructive_pointfree/lebesgue.ma b/helm/software/matita/dama/constructive_pointfree/lebesgue.ma
index 583dc638c2c9ee218d4b91fe2523ea00108818b9..1eb6e4aac306deb2fb1cb9f663b7f768c36071c5 100644 (file)
--- a/helm/software/matita/dama/constructive_pointfree/lebesgue.ma
+++ b/helm/software/matita/dama/constructive_pointfree/lebesgue.ma
@@ -14,62 +14,8 @@
 
 set "baseuri" "cic:/matita/lebesgue/".
 
-include "reals.ma".
-include "lattices.ma".
+include "metric_lattice.ma".
+include "sequence.ma".
 
-record measured_set (R : real) : Type ≝ {
-  ms_carr :> Type;
-  ms_measure: ms_carr → ms_carr → R
-}.
+(* Section 3.2 *)
 
-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;