From fdc6fe20875e45ea7446516af8904e2fb9b15388 Mon Sep 17 00:00:00 2001
From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Tue, 6 Jan 2009 02:05:57 +0000
Subject: [PATCH] Basic pairs restored; require renaming to use them together
 with o-basic_pairs.

---
 .../formal_topology/overlap/basic_pairs.ma    | 73 ++++++++++---------
 1 file changed, 40 insertions(+), 33 deletions(-)

diff --git a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
index 4d467fc26..071892f6b 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
@@ -40,27 +40,6 @@ notation "hvbox (r \sub \f)"  with precedence 90 for @{'form_rel $r}.
 interpretation "concrete relation" 'concr_rel r = (concr_rel __ r). 
 interpretation "formal relation" 'form_rel r = (form_rel __ r).
 
-include "o-basic_pairs.ma".
-(* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
-definition o_basic_pair_of_basic_pair: cic:/matita/formal_topology/basic_pairs/basic_pair.ind#xpointer(1/1) → basic_pair.
- intro;
- constructor 1;
-  [ apply (SUBSETS (concr b));
-  | apply (SUBSETS (form b));
-  | apply (orelation_of_relation ?? (rel b)); ]
-qed.
-
-definition o_relation_pair_of_relation_pair:
- ∀BP1,BP2.cic:/matita/formal_topology/basic_pairs/relation_pair.ind#xpointer(1/1) BP1 BP2 →
-  relation_pair (o_basic_pair_of_basic_pair BP1) (o_basic_pair_of_basic_pair BP2).
- intros;
- constructor 1;
-  [ apply (orelation_of_relation ?? (r \sub \c));
-  | apply (orelation_of_relation ?? (r \sub \f));
-  |
-  ]
-qed.
-
 definition relation_pair_equality:
  ∀o1,o2. equivalence_relation1 (relation_pair o1 o2).
  intros;
@@ -118,23 +97,26 @@ definition relation_pair_composition:
      | apply (r1 \sub\f ∘ r \sub\f)
      | lapply (commute ?? r) as H;
        lapply (commute ?? r1) as H1;
-       apply (.= ASSOC1);
+       alias symbol "trans" = "trans1".
+       alias symbol "assoc" = "category1 assoc".
+       apply (.= ASSOC);
        apply (.= #‡H1);
-       apply (.= ASSOC1\sup -1);
+       alias symbol "invert" = "setoid1 symmetry".
+       apply (.= ASSOC ^ -1);
        apply (.= H‡#);
-       apply ASSOC1]
+       apply ASSOC]
   | intros;
     change with (⊩ ∘ (b\sub\c ∘ a\sub\c) = ⊩ ∘ (b'\sub\c ∘ a'\sub\c));  
-    change in H with (⊩ ∘ a \sub\c = ⊩ ∘ a' \sub\c);
-    change in H1 with (⊩ ∘ b \sub\c = ⊩ ∘ b' \sub\c);
-    apply (.= ASSOC1);
-    apply (.= #‡H1);
+    change in e with (⊩ ∘ a \sub\c = ⊩ ∘ a' \sub\c);
+    change in e1 with (⊩ ∘ b \sub\c = ⊩ ∘ b' \sub\c);
+    apply (.= ASSOC);
+    apply (.= #‡e1);
     apply (.= #‡(commute ?? b'));
-    apply (.= ASSOC1 \sup -1);
-    apply (.= H‡#);
-    apply (.= ASSOC1);
+    apply (.= ASSOC ^ -1);
+    apply (.= e‡#);
+    apply (.= ASSOC);
     apply (.= #‡(commute ?? b')\sup -1);
-    apply (ASSOC1 \sup -1)]
+    apply (ASSOC ^ -1)]
 qed.
     
 definition BP: category1.
@@ -146,7 +128,9 @@ definition BP: category1.
   | intros;
     change with (⊩ ∘ (a34\sub\c ∘ (a23\sub\c ∘ a12\sub\c)) =
                  ⊩ ∘ ((a34\sub\c ∘ a23\sub\c) ∘ a12\sub\c));
-    apply (ASSOC1‡#);
+    alias symbol "refl" = "refl1".
+    alias symbol "prop2" = "prop21".
+    apply (ASSOC‡#);
   | intros;
     change with (⊩ ∘ (a\sub\c ∘ (id_relation_pair o1)\sub\c) = ⊩ ∘ a\sub\c);
     apply ((id_neutral_right1 ????)‡#);
@@ -155,6 +139,7 @@ definition BP: category1.
     apply ((id_neutral_left1 ????)‡#);]
 qed.
 
+(*
 definition BPext: ∀o: BP. form o ⇒ Ω \sup (concr o).
  intros; constructor 1;
   [ apply (ext ? ? (rel o));
@@ -199,3 +184,25 @@ qed.
 
 interpretation "basic pair relation for subsets" 'Vdash2 x y = (fun1 (concr _) __ (relS _) x y).
 interpretation "basic pair relation for subsets (non applied)" 'Vdash = (fun1 ___ (relS _)).
+*)
+
+include "o-basic_pairs.ma".
+(* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
+definition o_basic_pair_of_basic_pair: cic:/matita/formal_topology/basic_pairs/basic_pair.ind#xpointer(1/1) → basic_pair.
+ intro;
+ constructor 1;
+  [ apply (SUBSETS (concr b));
+  | apply (SUBSETS (form b));
+  | apply (orelation_of_relation ?? (rel b)); ]
+qed.
+
+definition o_relation_pair_of_relation_pair:
+ ∀BP1,BP2.cic:/matita/formal_topology/basic_pairs/relation_pair.ind#xpointer(1/1) BP1 BP2 →
+  relation_pair (o_basic_pair_of_basic_pair BP1) (o_basic_pair_of_basic_pair BP2).
+ intros;
+ constructor 1;
+  [ apply (orelation_of_relation ?? (r \sub \c));
+  | apply (orelation_of_relation ?? (r \sub \f));
+  |
+  ]
+qed.
\ No newline at end of file
-- 
2.39.2