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[helm.git] / helm / software / matita / library / formal_topology / basic_topologies_to_o-basic_topologies.ma

diff --git a/helm/software/matita/library/formal_topology/basic_topologies_to_o-basic_topologies.ma b/helm/software/matita/library/formal_topology/basic_topologies_to_o-basic_topologies.ma
index 0d997a5af617cf67b7947bc8fc5fe91cfb695ca8..58b75fb680ececa60755fcb2e77b7105b9245254 100644 (file)
--- a/helm/software/matita/library/formal_topology/basic_topologies_to_o-basic_topologies.ma
+++ b/helm/software/matita/library/formal_topology/basic_topologies_to_o-basic_topologies.ma
@@ -49,63 +49,43 @@ definition BTop_to_OBTop: carr3 ((category2_of_category1 BTop) ⇒_\c3 OBTop).
   | cases daemon (*apply o_relation_topology_of_relation_topology_morphism_respects_comp*);]
 qed.
 
-(* FIXME
-alias symbol "eq" (instance 2) = "setoid1 eq".
-alias symbol "eq" (instance 1) = "setoid2 eq".
 theorem BTop_to_OBTop_faithful: faithful2 ?? BTop_to_OBTop.
- intros 5;
- whd in e; unfold BTop_to_OBTop in e; simplify in e;
- change in match (oA ?) in e with (A o1);
- whd in f g;
- alias symbol "OR_f_minus_star" (instance 1) = "relation f⎻*".
- change in match ((o_continuous_relation_of_continuous_relation_morphism o1 o2 f)⎻* ) in e with ((foo ?? f)⎻* );
- change in match ((o_continuous_relation_of_continuous_relation_morphism o1 o2 g)⎻* ) in e with ((foo ?? g)⎻* );
- whd; whd in o1 o2;
- intro b;
- alias symbol "OR_f_minus" (instance 1) = "relation f⎻".
- letin fb ≝ ((ext ?? f) b);
- lapply (e fb);
- whd in Hletin:(? ? ? % %);
- cases (Hletin); simplify in s s1;
- split;
-  [2: intro; simplify;
-    lapply depth=0 (s b); intro; apply (Hletin1 ? a ?)
-     [ 2: whd in f1;
- change in Hletin with ((foo ?? f)⎻*
- 
- alias symbol "OR_f_minus_star" (instance 4) = "relation f⎻*".
- alias symbol "OR_f_minus_star" (instance 4) = "relation f⎻*".
-change in e with
- (comp2 SET1 (Ω^o1) (Ω^o1) (Ω^o2) (A o1) (foo o1 o2 f)⎻* =_1
-  comp2 SET1 (Ω^o1) (Ω^o1) (Ω^o2) (A o1) (foo o1 o2 g)⎻*
- );
- 
- 
- 
- change in e with (comp1 SET (Ω^o1) ?? (A o1) (foo o1 o2 f)⎻*  = ((foo o1 o2 g)⎻* ∘ A o1));
- unfold o_continuous_relation_of_continuous_relation_morphism in e;
- unfold o_continuous_relation_of_continuous_relation in e;
- simplify in e;
+ intros 5; apply (continuous_relation_eq_inv' o1 o2 f g); apply e;
 qed.
 
 include "formal_topology/notation.ma".
 
-theorem BTop_to_OBTop_full: 
-   ∀S,T.∀f. exT22 ? (λg. map_arrows2 ?? BTop_to_OBTop S T g = f).
- intros;
+theorem BTop_to_OBTop_full: full2 ?? BTop_to_OBTop.
+ intros 3 (S T);
  cases (POW_full (carrbt S) (carrbt T) (Ocont_rel ?? f)) (g Hg);
- exists[
+ (* cases Hg; *)
+ exists [
    constructor 1;
     [ apply g
-    | apply hide; intros; lapply (Oreduced ?? f ? e);
+    | unfold image_coercion; cases daemon (*apply hide; intros; lapply (Oreduced ?? f ? e); unfold image_coercion;
       cases Hg; lapply (e3 U) as K; apply (.= K);
-      apply (.= Hletin); apply rule (†(K^-1));
-    | apply hide; intros; lapply (Osaturated ?? f ? e);
+      apply (.= Hletin); apply rule (†(K^-1)); *)
+    | cases daemon (* apply hide; intros; lapply (Osaturated ?? f ? e);
       cases Hg; lapply (e1 U) as K; apply (.= K);
-      apply (.= Hletin); apply rule (†(K^-1));
+      apply (.= Hletin); apply rule (†(K^-1)); *)
     ]
  | simplify; unfold BTop_to_OBTop; simplify;
+   cases Hg; unfold o_continuous_relation_of_continuous_relation_morphism;
+   simplify;
+   change with ((orelation_of_relation ?? g)⎻* ∘ oA (o_basic_topology_of_basic_topology S) =
+                f⎻* ∘ oA (o_basic_topology_of_basic_topology S));
+
+   
+   change with (g⎻* ∘ oA (o_basic_topology_of_basic_topology S) =
+                f⎻* ∘ oA (o_basic_topology_of_basic_topology S));
+   apply sym2; whd in T;
+   intro;
+   apply trans2; [2: apply sym2; [2: apply Hg;
+   
+   whd in ⊢ (?(??%%)???);
+    apply (.= Hg^-1);
    unfold o_continuous_relation_of_continuous_relation_morphism; simplify;
-   cases Hg; whd; simplify; intro; 
+   intro; simplify;
+   unfold image_coercion; cases Hg; whd; simplify; intro; simplify;
 qed.
 *)