X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fo-basic_pairs_to_o-basic_topologies.ma;h=b2dfffd02952995536a22a7710c54ff9984c8552;hb=d4cd2564126b15d4f0aa736353d25dfc34d2cad8;hp=bdadaf0fe376a197d162194faefb3dac21e69166;hpb=5ab72ef7c6da38f9bc239e13f049521922987183;p=helm.git

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs_to_o-basic_topologies.ma b/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs_to_o-basic_topologies.ma
index bdadaf0fe..b2dfffd02 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs_to_o-basic_topologies.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs_to_o-basic_topologies.ma
@@ -12,19 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "notation.ma".
 include "o-basic_pairs.ma".
 include "o-basic_topologies.ma".
 
 alias symbol "eq" = "setoid1 eq".
 
 (* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
-definition o_basic_topology_of_o_basic_pair: BP → BTop.
+definition o_basic_topology_of_o_basic_pair: OBP → BTop.
  intro t;
  constructor 1;
-  [ apply (form t);
+  [ apply (Oform t);
   | apply (□_t ∘ Ext⎽t);
   | apply (◊_t ∘ Rest⎽t);
-  | intros 2; split; intro;
+  | apply hide; intros 2; split; intro;
      [ change with ((⊩) \sup ⎻* ((⊩) \sup ⎻ U) ≤ (⊩) \sup ⎻* ((⊩) \sup ⎻ V));
        apply (. (#‡(lemma_10_4_a ?? (⊩) V)^-1));
        apply f_minus_star_image_monotone;
@@ -36,7 +37,7 @@ definition o_basic_topology_of_o_basic_pair: BP → BTop.
         | change with (U ≤ (⊩)⎻* ((⊩)⎻ U));
           apply (. (or_prop2 : ?) ^ -1);
           apply oa_leq_refl; ]]
-  | intros 2; split; intro;
+  | apply hide; intros 2; split; intro;
      [ change with (◊_t ((⊩) \sup * U) ≤ ◊_t ((⊩) \sup * V));
        apply (. ((lemma_10_4_b ?? (⊩) U)^-1)‡#);
        apply (f_image_monotone ?? (⊩) ? ((⊩)* V));
@@ -48,7 +49,7 @@ definition o_basic_topology_of_o_basic_pair: BP → BTop.
         | change with ((⊩) ((⊩)* V) ≤ V);
           apply (. (or_prop1 : ?));
           apply oa_leq_refl; ]]
-  | intros;
+  | apply hide; intros;
     apply (.= (oa_overlap_sym' : ?));
     change with ((◊_t ((⊩)* V) >< (⊩)⎻* ((⊩)⎻ U)) = (U >< (◊_t ((⊩)* V))));
     apply (.= (or_prop3 ?? (⊩) ((⊩)* V) ?));
@@ -58,37 +59,61 @@ definition o_basic_topology_of_o_basic_pair: BP → BTop.
 qed.
 
 definition o_continuous_relation_of_o_relation_pair:
- ∀BP1,BP2.arrows2 BP BP1 BP2 →
+ ∀BP1,BP2.arrows2 OBP BP1 BP2 →
   arrows2 BTop (o_basic_topology_of_o_basic_pair BP1) (o_basic_topology_of_o_basic_pair BP2).
  intros (BP1 BP2 t);
  constructor 1;
   [ apply (t \sub \f);
-  | unfold o_basic_topology_of_o_basic_pair; simplify; intros;
+  | apply hide; unfold o_basic_topology_of_o_basic_pair; simplify; intros;
     apply sym1;
-    unfold in ⊢ (? ? ? (? ? ? ? %) ?);
     apply (.= †(†e));
     change in ⊢ (? ? ? (? ? ? ? %) ?) with ((t \sub \f ∘ (⊩)) ((⊩)* U));
     cut ((t \sub \f ∘ (⊩)) ((⊩)* U) = ((⊩) ∘ t \sub \c) ((⊩)* U)) as COM;[2:
-      cases (commute ?? t); apply (e3 ^ -1 ((⊩)* U));]
+      cases (Ocommute ?? t); apply (e3 ^ -1 ((⊩)* U));]
     apply (.= †COM);
     change in ⊢ (? ? ? % ?) with (((⊩) ∘ (⊩)* ) (((⊩) ∘ t \sub \c ∘ (⊩)* ) U));
     apply (.= (lemma_10_3_c ?? (⊩) (t \sub \c ((⊩)* U))));
     apply (.= COM ^ -1);
     change in ⊢ (? ? ? % ?) with (t \sub \f (((⊩) ∘ (⊩)* ) U));
     change in e with (U=((⊩)∘(⊩ \sub BP1) \sup * ) U);
-    unfold in ⊢ (? ? ? % %); apply (†e^-1);
-  | unfold o_basic_topology_of_o_basic_pair; simplify; intros;
+    apply (†e^-1);
+  | apply hide; unfold o_basic_topology_of_o_basic_pair; simplify; intros;
     apply sym1;
-    unfold in ⊢ (? ? ? (? ? ? ? %) ?);
     apply (.= †(†e));
     change in ⊢ (? ? ? (? ? ? ? %) ?) with ((t \sub \f⎻* ∘ (⊩)⎻* ) ((⊩)⎻ U));
     cut ((t \sub \f⎻* ∘ (⊩)⎻* ) ((⊩)⎻ U) = ((⊩)⎻* ∘ t \sub \c⎻* ) ((⊩)⎻ U)) as COM;[2:
-      cases (commute ?? t); apply (e1 ^ -1 ((⊩)⎻ U));]
+      cases (Ocommute ?? t); apply (e1 ^ -1 ((⊩)⎻ U));]
     apply (.= †COM);
     change in ⊢ (? ? ? % ?) with (((⊩)⎻* ∘ (⊩)⎻ ) (((⊩)⎻* ∘ t \sub \c⎻* ∘ (⊩)⎻ ) U));
     apply (.= (lemma_10_3_d ?? (⊩) (t \sub \c⎻* ((⊩)⎻ U))));
     apply (.= COM ^ -1);
     change in ⊢ (? ? ? % ?) with (t \sub \f⎻* (((⊩)⎻* ∘ (⊩)⎻ ) U));
     change in e with (U=((⊩)⎻* ∘(⊩ \sub BP1)⎻ ) U);
-    unfold in ⊢ (? ? ? % %); apply (†e^-1);]
-qed.
\ No newline at end of file
+    apply (†e^-1);]
+qed.
+
+
+definition OR : carr3 (arrows3 CAT2 OBP BTop).
+constructor 1;
+[ apply o_basic_topology_of_o_basic_pair;
+| intros; constructor 1;
+  [ apply o_continuous_relation_of_o_relation_pair;
+  | apply hide; 
+    intros; whd; unfold o_continuous_relation_of_o_relation_pair; simplify;;
+    change with ((a \sub \f ⎻* ∘ A (o_basic_topology_of_o_basic_pair S)) =
+                 (a' \sub \f ⎻*∘A (o_basic_topology_of_o_basic_pair S)));
+    whd in e; cases e; clear e e2 e3 e4;
+    change in ⊢ (? ? ? (? ? ? ? ? % ?) ?) with ((⊩\sub S)⎻* ∘ (⊩\sub S)⎻);
+    apply (.= (comp_assoc2 ? ???? ?? a\sub\f⎻* ));
+    change in ⊢ (? ? ? (? ? ? ? ? ? %) ?) with (a\sub\f ∘ ⊩\sub S)⎻*;
+    apply (.= #‡†(Ocommute:?)^-1);
+    apply (.= #‡e1);
+    change in ⊢ (? ? ? (? ? ? ? ? ? %) ?) with (⊩\sub T ∘ a'\sub\c)⎻*;
+    apply (.= #‡†(Ocommute:?));    
+    change in ⊢ (? ? ? (? ? ? ? ? ? %) ?) with (a'\sub\f⎻* ∘ (⊩\sub S)⎻* );    
+    apply (.= (comp_assoc2 ? ???? ?? a'\sub\f⎻* )^-1);
+    apply refl2;]
+| intros 2 (o a); apply rule #;
+| intros 6; apply refl1;]
+qed.
+