...

[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 0bc8a32255cde1804c708a588c4f25f772215ed6..e724dc2e6ba4b7613b011973f483f89109096b63 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
+++ b/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
@@ -36,7 +36,7 @@ record ordered_uniform_space : Type ≝ {
   ous_stuff :> ordered_uniform_space_;
   ous_convex: ∀U.us_unifbase ous_stuff U → convex ous_stuff U
 }.   
-
+(*
 definition Type_of_ordered_uniform_space : ordered_uniform_space → Type.
 intro; compose ordered_set_OF_ordered_uniform_space with os_l.
 apply (hos_carr (f o));
@@ -47,9 +47,9 @@ intro; compose ordered_set_OF_ordered_uniform_space with os_r.
 apply (hos_carr (f o));
 qed.
 
-coercion Type_of_ordered_uniform_space.
 coercion Type_of_ordered_uniform_space_dual.
-
+coercion Type_of_ordered_uniform_space.
+*)
 definition half_ordered_set_OF_ordered_uniform_space : ordered_uniform_space → half_ordered_set.
 intro; compose ordered_set_OF_ordered_uniform_space with os_l. apply (f o);
 qed.
@@ -143,39 +143,39 @@ intros (O l r); apply mk_ordered_uniform_space;
         [1: intros (U H); intro x; simplify; 
             cases H (w Hw); cases Hw (Gw Hwp); clear H Hw; intro Hm;
             lapply (us_phi1 O w Gw x Hm) as IH;
-            apply (restrict ? l r ??? Hwp IH); STOP
+            apply (restrict ? l r ??? Hwp IH); 
         |2: intros (U V HU HV); cases HU (u Hu); cases HV (v Hv); clear HU HV;
             cases Hu (Gu HuU); cases Hv (Gv HvV); clear Hu Hv;
-            cases (us_phi2 ??? Gu Gv) (w HW); cases HW (Gw Hw); clear HW;
-            exists; [apply (λb:{[l,r]} square.w b)] split;
+            cases (us_phi2 O u v Gu Gv) (w HW); cases HW (Gw Hw); clear HW;
+            exists; [apply (λb:{[l,r]} squareB.w b)] split;
             [1: unfold f; simplify; clearbody f;
                 exists; [apply w]; split; [assumption] intro b; simplify;
                 unfold segment_square_of_ordered_set_square;
                 cases b; intros; split; intros; assumption;
             |2: intros 2 (x Hx); cases (Hw ? Hx); split;
-                [apply (restrict ?????? HuU H)|apply (restrict ?????? HvV H1);]]
+                [apply (restrict O l r ??? HuU H)|apply (restrict O l r ??? HvV H1);]]
         |3: intros (U Hu); cases Hu (u HU); cases HU (Gu HuU); clear Hu HU;
-            cases (us_phi3 ?? Gu) (w HW); cases HW (Gw Hwu); clear HW;
-            exists; [apply (λx:{[l,r]} square.w x)] split;
+            cases (us_phi3 O u Gu) (w HW); cases HW (Gw Hwu); clear HW;
+            exists; [apply (λx:{[l,r]} squareB.w x)] split;
             [1: exists;[apply w];split;[assumption] intros; simplify; intro;
                 unfold segment_square_of_ordered_set_square;
                 cases b; intros; split; intro; assumption;
-            |2: intros 2 (x Hx); apply (restrict ?????? HuU); apply Hwu; 
+            |2: intros 2 (x Hx); apply (restrict O l r ??? HuU); apply Hwu; 
                 cases Hx (m Hm); exists[apply (\fst m)] apply Hm;]
         |4: intros (U HU x); cases HU (u Hu); cases Hu (Gu HuU); clear HU Hu;
-            cases (us_phi4 ?? Gu x) (Hul Hur);
+            cases (us_phi4 O u Gu x) (Hul Hur);
             split; intros; 
-            [1: lapply (invert_restriction_agreement ????? HuU) as Ra;
-                apply (restrict ????? x Ra);
-                apply Hul; apply (unrestrict ?????? HuU H);
-            |2: apply (restrict ?????? HuU); apply Hur; 
-                apply (unrestrict ?????? (invert_restriction_agreement ????? HuU) H);]]
+            [1: lapply (invert_restriction_agreement O l r ?? HuU) as Ra;
+                apply (restrict O l r ?? x Ra);
+                apply Hul; apply (unrestrict O l r ??? HuU H);
+            |2: apply (restrict O l r ??? HuU); apply Hur; 
+                apply (unrestrict O l r ??? (invert_restriction_agreement O l r ?? HuU) H);]]
     |2: simplify; reflexivity;]
 |2: simplify; unfold convex; intros;
     cases H (u HU); cases HU (Gu HuU); clear HU H; 
-    lapply (ous_convex ?? Gu (bs_of_ss ? l r p) ? H2 (bs_of_ss ? l r y) H3) as Cu;
-    [1: apply (unrestrict ?????? HuU); apply H1;
-    |2: apply (restrict ?????? HuU Cu);]]
+    lapply (ous_convex ?? Gu p ? H2 y H3) as Cu;
+    [1: apply (unrestrict O l r ??? HuU); apply H1;
+    |2: apply (restrict O l r ??? HuU Cu);]]
 qed.
 
 interpretation "Ordered uniform space segment" 'segment_set a b = 
@@ -185,9 +185,10 @@ interpretation "Ordered uniform space segment" 'segment_set a b =
 alias symbol "pi1" = "exT \fst".
 lemma restric_uniform_convergence:
  ∀O:ordered_uniform_space.∀l,u:O.
-  ∀x:{[l,u]}.
-   ∀a:sequence {[l,u]}.
-     ⌊n,\fst (a n)⌋ uniform_converges (\fst x) → 
+  ∀x:(segment_ordered_uniform_space O l u).
+   ∀a:sequence (segment_ordered_uniform_space O l u).
+     uniform_converge (segment_ordered_uniform_space O l u) 
+     (mk_seq O (λn:nat.\fst (a n))) (\fst x) → True. 
       a uniform_converges x.
 intros 8; cases H1; cases H2; clear H2 H1;
 cases (H ? H3) (m Hm); exists [apply m]; intros;