From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Sat, 3 Jan 2009 16:16:09 +0000 (+0000)
Subject: More reorganization.
X-Git-Tag: make_still_working~4308
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=1c406089d385be2d444308a783bc051bd28be463;p=helm.git

More reorganization.
---

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index ea246ef6c..f09e0ee6c 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -181,6 +181,7 @@ interpretation "prop11" 'prop1 c = (prop11 _____ c).
 interpretation "prop12" 'prop1 c = (prop12 _____ c).
 interpretation "prop2" 'prop2 l r = (prop2 ________ l r).
 interpretation "prop21" 'prop2 l r = (prop21 ________ l r).
+interpretation "prop22" 'prop2 l r = (prop22 ________ l r).
 interpretation "refl" 'refl = (refl ___).
 interpretation "refl1" 'refl = (refl1 ___).
 interpretation "refl2" 'refl = (refl2 ___).
@@ -288,8 +289,8 @@ notation "'ASSOC'" with precedence 90 for @{'assoc}.
 notation "'ASSOC1'" with precedence 90 for @{'assoc1}.
 notation "'ASSOC2'" with precedence 90 for @{'assoc2}.
 
-interpretation "category1 composition" 'compose x y = (fun22 ___ (comp2 ____) y x).
-interpretation "category1 assoc" 'assoc1 = (comp_assoc2 ________).
+interpretation "category2 composition" 'compose x y = (fun22 ___ (comp2 ____) y x).
+interpretation "category2 assoc" 'assoc1 = (comp_assoc2 ________).
 interpretation "category1 composition" 'compose x y = (fun21 ___ (comp1 ____) y x).
 interpretation "category1 assoc" 'assoc1 = (comp_assoc1 ________).
 interpretation "category composition" 'compose x y = (fun2 ___ (comp ____) y x).
@@ -387,10 +388,18 @@ definition prop11_SET1 :
 intros; apply (prop11 A B w a b e);
 qed.
 
-definition hint: Type_OF_category2 SET1 → Type1.
+definition setoid2_OF_category2: Type_OF_category2 SET1 → setoid2.
+ intro; apply (setoid2_of_setoid1 t); qed.
+coercion setoid2_OF_category2.
+
+definition objs2_OF_category1: Type_OF_category1 SET → objs2 SET1.
+ intro; apply (setoid1_of_setoid t); qed.
+coercion objs2_OF_category1.
+
+definition Type1_OF_SET1: Type_OF_category2 SET1 → Type1.
  intro; whd in t; apply (carr1 t);
 qed.
-coercion hint.
+coercion Type1_OF_SET1.
 
 interpretation "SET dagger" 'prop1 h = (prop11_SET1 _ _ _ _ _ h).
 interpretation "unary morphism1" 'Imply a b = (arrows2 SET1 a b).
diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
index ce9583da3..029e93258 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
@@ -49,14 +49,6 @@ interpretation "unary morphism comprehension with proof" 'comprehension_by s \et
 interpretation "unary morphism1 comprehension with proof" 'comprehension_by s \eta.f p = 
   (mk_unary_morphism1 s _ f p).
 
-definition hint: Type_OF_category2 SET1 → setoid2.
- intro; apply (setoid2_of_setoid1 t); qed.
-coercion hint.
-
-definition hint2: Type_OF_category1 SET → objs2 SET1.
- intro; apply (setoid1_of_setoid t); qed.
-coercion hint2.
-
 (* per il set-indexing vedere capitolo BPTools (foundational tools), Sect. 0.3.4 complete
    lattices, Definizione 0.9 *)
 (* USARE L'ESISTENZIALE DEBOLE *)
@@ -147,7 +139,11 @@ for @{ 'oa_meet_bin $a $b }.
 interpretation "o-algebra binary meet" 'oa_meet_bin a b = 
   (fun21 ___ (binary_meet _) a b).
 
+coercion Type1_OF_OAlgebra nocomposites.
+
 lemma oa_overlap_preservers_meet: ∀O:OAlgebra.∀p,q:O.p >< q → p >< (p ∧ q).
+(* next change to avoid universe inconsistency *)
+change in ⊢ (?→%→%→?) with (Type1_OF_OAlgebra O);
 intros;  lapply (oa_overlap_preserves_meet_ O p q f);
 lapply (prop21 O O CPROP (oa_overlap O) p p ? (p ∧ q) # ?);
 [3: apply (if ?? (Hletin1)); apply Hletin;|skip] apply refl1;
@@ -239,28 +235,29 @@ qed.
 
 coercion arrows1_OF_ORelation_setoid.
 
-lemma umorphism_OF_ORelation_setoid : ∀P,Q. ORelation_setoid P Q → P ⇒ Q.
+lemma umorphism_OF_ORelation_setoid : ∀P,Q. ORelation_setoid P Q → unary_morphism1 P Q.
 intros; apply (or_f ?? t);
 qed.
 
 coercion umorphism_OF_ORelation_setoid.
 
+lemma umorphism_setoid_OF_ORelation_setoid : ∀P,Q. ORelation_setoid P Q → unary_morphism1_setoid1 P Q.
+intros; apply (or_f ?? t);
+qed.
+
+coercion umorphism_setoid_OF_ORelation_setoid.
 
-lemma uncurry_arrows : ∀B,C. arrows1 SET B C → B → C. 
-intros; apply ((fun1 ?? t) t1);
+lemma uncurry_arrows : ∀B,C. ORelation_setoid B C → B → C. 
+intros; apply ((fun11 ?? t) t1);
 qed.
 
 coercion uncurry_arrows 1.
 
-lemma hint6 : ∀P,Q. arrows1 SET P Q → P ⇒ Q. intros; apply t;qed.
+lemma hint6: ∀P,Q. Type_OF_setoid2 (hint5 P ⇒ hint5 Q) → unary_morphism1 P Q.
+ intros; apply t;
+qed.
 coercion hint6.
 
-(*
-lemma hint2: OAlgebra → setoid. intros; apply (oa_P o). qed.
-coercion hint2 nocomposites.
-*)
-
-
 notation "r \sup *" non associative with precedence 90 for @{'OR_f_star $r}.
 notation > "r *" non associative with precedence 90 for @{'OR_f_star $r}.
 
@@ -290,13 +287,13 @@ intros; apply (or_prop3_ ?? F p q);
 qed.
 
 definition ORelation_composition : ∀P,Q,R. 
-  binary_morphism1 (ORelation_setoid P Q) (ORelation_setoid Q R) (ORelation_setoid P R).
+  binary_morphism2 (ORelation_setoid P Q) (ORelation_setoid Q R) (ORelation_setoid P R).
 intros;
 constructor 1;
 [ intros (F G);
   constructor 1;
   [ apply (G ∘ F);
-  | apply (G⎻* ∘ F⎻* );
+  | apply rule (G⎻* ∘ F⎻* );
   | apply (F* ∘ G* );
   | apply (F⎻ ∘ G⎻);
   | intros; 
@@ -312,24 +309,29 @@ constructor 1;
     apply or_prop3;
   ]
 | intros; split; simplify; 
-   [1,3: unfold arrows1_OF_ORelation_setoid; apply ((†H)‡(†H1));
-   |2,4: apply ((†H1)‡(†H));]]
+   [1,3: unfold umorphism_setoid_OF_ORelation_setoid; unfold arrows1_OF_ORelation_setoid; apply ((†e)‡(†e1));
+   |2,4: apply ((†e1)‡(†e));]]
 qed.
 
-definition OA : category1.
+definition OA : category2.
 split;
 [ apply (OAlgebra);
 | intros; apply (ORelation_setoid o o1);
 | intro O; split;
-  [1,2,3,4: apply id1;
+  [1,2,3,4: apply id2;
   |5,6,7:intros; apply refl1;] 
 | apply ORelation_composition;
 | intros (P Q R S F G H); split;
    [ change with (H⎻* ∘ G⎻* ∘ F⎻* = H⎻* ∘ (G⎻* ∘ F⎻* ));
-     apply (comp_assoc1 ????? (F⎻* ) (G⎻* ) (H⎻* ));
-   | apply ((comp_assoc1 ????? (H⎻) (G⎻) (F⎻))^-1);
-   | apply ((comp_assoc1 ????? F G H)^-1);
-   | apply ((comp_assoc1 ????? H* G* F* ));]
-| intros; split; unfold ORelation_composition; simplify; apply id_neutral_left1;
-| intros; split; unfold ORelation_composition; simplify; apply id_neutral_right1;]
-qed.
\ No newline at end of file
+     apply (comp_assoc2 ????? (F⎻* ) (G⎻* ) (H⎻* ));
+   | apply ((comp_assoc2 ????? (H⎻) (G⎻) (F⎻))^-1);
+   | apply ((comp_assoc2 ????? F G H)^-1);
+   | apply ((comp_assoc2 ????? H* G* F* ));]
+| intros; split; unfold ORelation_composition; simplify; apply id_neutral_left2;
+| intros; split; unfold ORelation_composition; simplify; apply id_neutral_right2;]
+qed.
+
+lemma setoid1_of_OA: OA → setoid1.
+ intro; apply (oa_P t);
+qed.
+coercion setoid1_of_OA.
diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
index 22c8fbdea..0511edd34 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
@@ -16,28 +16,28 @@ include "o-algebra.ma".
 
 alias symbol "eq" = "setoid1 eq".
 definition is_saturation ≝
- λC:OA.λA:unary_morphism (oa_P C) (oa_P C).
+ λC:OA.λA:unary_morphism1 C C.
   ∀U,V. (U ≤ A V) = (A U ≤ A V).
 
 definition is_reduction ≝
- λC:OA.λJ:unary_morphism (oa_P C) (oa_P C).
+ λC:OA.λJ:unary_morphism1 C C.
     ∀U,V. (J U ≤ V) = (J U ≤ J V).
 
 theorem saturation_expansive: ∀C,A. is_saturation C A → ∀U. U ≤ A U.
- intros; apply (fi ?? (H ??)); apply (oa_leq_refl C).
+ intros; apply (fi ?? (i ??)); apply (oa_leq_refl C).
 qed.
 
 theorem saturation_monotone:
  ∀C,A. is_saturation C A →
   ∀U,V. U ≤ V → A U ≤ A V.
- intros; apply (if ?? (H ??)); apply (oa_leq_trans C);
+ intros; apply (if ?? (i ??)); apply (oa_leq_trans C);
   [apply V|3: apply saturation_expansive ]
  assumption.
 qed.
 
 theorem saturation_idempotent: ∀C,A. is_saturation C A → ∀U. 
- eq (oa_P C) (A (A U)) (A U).
+ eq1 C (A (A U)) (A U).
  intros; apply (oa_leq_antisym C);
-  [ apply (if ?? (H (A U) U)); apply (oa_leq_refl C).
+  [ apply (if ?? (i (A U) U)); apply (oa_leq_refl C).
   | apply saturation_expansive; assumption]
-qed.
+qed.
\ No newline at end of file