WIP

[helm.git] / helm / software / matita / contribs / dama / dama / ordered_uniform.ma

diff --git a/helm/software/matita/contribs/dama/dama/ordered_uniform.ma b/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
index 1f4f6f6867a772e8b37e21d91e1c02b7446c47a4..36ba2d287503736707f4911fe6407d6fcee08d27 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
+++ b/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
@@ -34,7 +34,8 @@ coercion ous_unifspace.
 
 record ordered_uniform_space : Type ≝ {
   ous_stuff :> ordered_uniform_space_;
-  ous_convex: ∀U.us_unifbase ous_stuff U → convex (os_l ous_stuff) U
+  ous_convex_l: ∀U.us_unifbase ous_stuff U → convex (os_l ous_stuff) U;
+  ous_convex_r: ∀U.us_unifbase ous_stuff U → convex (os_r ous_stuff) U
 }.   
 
 definition half_ordered_set_OF_ordered_uniform_space : ordered_uniform_space → half_ordered_set.
@@ -170,7 +171,7 @@ intros (O s); apply mk_ordered_uniform_space;
 |2: simplify; unfold convex; intros 3; cases s1; intros;
     (* TODO: x2sx is for ≰, we need one for ≤ *) 
     cases H (u HU); cases HU (Gu HuU); clear HU H;
-    lapply depth=0 (ous_convex ?? Gu 〈\fst h,\fst h1〉 ???????) as K3;
+    lapply depth=0 (ous_convex_l ?? Gu 〈\fst h,\fst h1〉 ???????) as K3;
     [2: intro; apply H2; apply (x2sx (os_l O) s h h1 H);
     |3: apply 〈\fst (\fst y),\fst (\snd y)〉;
     |4: intro; change in H with (\fst (\fst y) ≰ \fst h1); apply H3;
@@ -182,11 +183,27 @@ intros (O s); apply mk_ordered_uniform_space;
     |7: change with (\fst (\fst y) ≤ \fst (\snd y)); intro; apply H6;
         apply (x2sx (os_l O) s (\fst y) (\snd y) H);
     |8: apply (restrict O s U u y HuU K3);
-    |1: apply (unrestrict O s ?? 〈h,h1〉 HuU H1);]]  
+    |1: apply (unrestrict O s ?? 〈h,h1〉 HuU H1);]
+|3: simplify; unfold convex; intros 3; cases s1; intros; (* TODO *)
+    cases H (u HU); cases HU (Gu HuU); clear HU H;
+    lapply depth=0 (ous_convex_r ?? Gu 〈\fst h,\fst h1〉 ???????) as K3;
+    [2: intro; apply H2; apply (x2sx (os_r O) s h h1 H);
+    |3: apply 〈\fst (\fst y),\fst (\snd y)〉;
+    |4: intro; (*change in H with (\fst (\fst y) ≱ \fst h1);*) apply H3;
+        apply (x2sx (os_r O) s (\fst y) h1 H);
+    |5: (*change with (\fst h ≥ \fst (\fst y));*) intro; apply H4;
+        apply (x2sx (os_r O) s h (\fst y) H);
+    |6: (*change with (\fst (\snd y) ≤ \fst h1);*) intro; apply H5;
+        apply (x2sx (os_r O) s (\snd y) h1 H);
+    |7: (*change with (\fst (\fst y) ≤ \fst (\snd y));*) intro; apply H6;
+        apply (x2sx (os_r O) s (\fst y) (\snd y) H);
+    |8: apply (restrict O s U u y HuU K3);
+    |1: apply (unrestrict O s ?? 〈h,h1〉 HuU H1);]
+]  
 qed.
 
-interpretation "Ordered uniform space segment" 'segment_set a b = 
- (segment_ordered_uniform_space _ a b).
+interpretation "Ordered uniform space segment" 'segset a = 
+ (segment_ordered_uniform_space _ a).
 
 (* Lemma 3.2 *)
 alias symbol "pi1" = "exT \fst".
@@ -196,9 +213,9 @@ lemma restric_uniform_convergence:
    ∀a:sequence {[s]}.
     (⌊n, \fst (a n)⌋ : sequence O) uniform_converges (\fst x) → 
       a uniform_converges x.
-intros 8; cases H1; cases H2; clear H2 H1;
+intros 7; cases H1; cases H2; clear H2 H1;
 cases (H ? H3) (m Hm); exists [apply m]; intros; 
-apply (restrict ? l u ??? H4); apply (Hm ? H1);
+apply (restrict ? s ??? H4); apply (Hm ? H1);
 qed.
 
 definition order_continuity ≝