From 759451f66c0009b12e5bcc9fe0c61f7ab5277057 Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Thu, 8 Jan 2009 16:48:36 +0000
Subject: [PATCH] eq over SET1 and SET no longer used

---
 .../formal_topology/overlap/categories.ma     | 57 +------------------
 1 file changed, 1 insertion(+), 56 deletions(-)

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index 2582167dc..0ac3b518b 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -54,7 +54,6 @@ definition setoid1_of_setoid: setoid → setoid1.
     | apply (trans s)]]
 qed.
 
-(* questa coercion e' necessaria per problemi di unificazione *)
 coercion setoid1_of_setoid.
 
 definition reflexive2: ∀A:Type2.∀R:A→A→CProp2.CProp2 ≝ λA:Type2.λR:A→A→CProp2.∀x:A.R x x.
@@ -87,24 +86,6 @@ qed.
 
 coercion setoid2_of_setoid1.
 
-(*
-definition Leibniz: Type → setoid.
- intro;
- constructor 1;
-  [ apply T
-  | constructor 1;
-     [ apply (λx,y:T.cic:/matita/logic/equality/eq.ind#xpointer(1/1) ? x y)
-     | alias id "refl_eq" = "cic:/matita/logic/equality/eq.ind#xpointer(1/1/1)".
-       apply refl_eq
-     | alias id "sym_eq" = "cic:/matita/logic/equality/sym_eq.con".
-       apply sym_eq
-     | alias id "trans_eq" = "cic:/matita/logic/equality/trans_eq.con".
-       apply trans_eq ]]
-qed.
-
-coercion Leibniz.
-*)
-
 interpretation "setoid2 eq" 'eq x y = (eq_rel2 _ (eq2 _) x y).
 interpretation "setoid1 eq" 'eq x y = (eq_rel1 _ (eq1 _) x y).
 interpretation "setoid eq" 'eq x y = (eq_rel _ (eq _) x y).
@@ -210,21 +191,6 @@ definition if_morphism: binary_morphism1 CPROP CPROP CPROP.
      | apply (fi ?? e1); apply f; apply (if ?? e); assumption]]
 qed.
 
-(*
-definition eq_morphism: ∀S:setoid. binary_morphism S S CPROP.
- intro;
- constructor 1;
-  [ apply (eq_rel ? (eq S))
-  | intros; split; intro;
-     [ apply (.= H \sup -1);
-       apply (.= H2);
-       assumption
-     | apply (.= H);
-       apply (.= H2);
-       apply (H1 \sup -1)]]
-qed.
-*)
-
 record category : Type1 ≝
  { objs:> Type0;
    arrows: objs → objs → setoid;
@@ -267,8 +233,6 @@ interpretation "category1 assoc" 'assoc = (comp_assoc1 ________).
 interpretation "category composition" 'compose x y = (fun2 ___ (comp ____) y x).
 interpretation "category assoc" 'assoc = (comp_assoc ________).
 
-(* bug grande come una casa?
-   Ma come fa a passare la quantificazione larga??? *)
 definition unary_morphism_setoid: setoid → setoid → setoid.
  intros;
  constructor 1;
@@ -305,18 +269,8 @@ definition setoid1_of_SET: SET → setoid1.
 qed.
 coercion setoid1_of_SET.
 
-definition eq': ∀w:SET.equivalence_relation ? := λw.eq w.
-
-definition prop1_SET : 
- ∀A,B:SET.∀w:arrows1 SET A B.∀a,b:Type_OF_objs1 A.eq' ? a b→eq' ? (w a) (w b).
-intros; apply (prop1 A B w a b e);
-qed.
-
-
-interpretation "SET dagger" 'prop1 h = (prop1_SET _ _ _ _ _ h).
 notation "hbox(a break ⇒ b)" right associative with precedence 20 for @{ 'Imply $a $b }.
 interpretation "unary morphism" 'Imply a b = (arrows1 SET a b).
-interpretation "SET eq" 'eq x y = (eq_rel _ (eq' _) x y).
 
 definition unary_morphism1_setoid1: setoid1 → setoid1 → setoid1.
  intros;
@@ -351,14 +305,7 @@ definition setoid1_OF_SET1: objs2 SET1 → setoid1.
  intros; apply o; qed.
 
 coercion setoid1_OF_SET1.
-
-definition eq'': ∀w:SET1.equivalence_relation1 ? := λw.eq1 w.
-
-definition prop11_SET1 : 
- ∀A,B:SET1.∀w:arrows2 SET1 A B.∀a,b:Type_OF_objs2 A.eq'' ? a b→eq'' ? (w a) (w b).
-intros; apply (prop11 A B w a b e);
-qed.
-
+ 
 definition setoid2_OF_category2: Type_OF_category2 SET1 → setoid2.
  intro; apply (setoid2_of_setoid1 t); qed.
 coercion setoid2_OF_category2.
@@ -378,9 +325,7 @@ definition Type_OF_setoid1_of_carr: ∀U. carr U → Type_OF_setoid1 ?(*(setoid1
 qed.
 coercion Type_OF_setoid1_of_carr.
 
-interpretation "SET dagger" 'prop1 h = (prop11_SET1 _ _ _ _ _ h).
 interpretation "unary morphism1" 'Imply a b = (arrows2 SET1 a b).
-interpretation "SET1 eq" 'eq x y = (eq_rel1 _ (eq'' _) x y).
 
 lemma unary_morphism1_of_arrows1_SET1: ∀S,T. (S ⇒ T) → unary_morphism1 S T.
  intros; apply t;
-- 
2.39.2