after a PITA, lebergue is dualized!

[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 e724dc2e6ba4b7613b011973f483f89109096b63..8cca24c90b31c17bf67f90987d7cc72c57a768fe 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
+++ b/helm/software/matita/contribs/dama/dama/ordered_uniform.ma
@@ -36,20 +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));
-qed.
-
-definition Type_of_ordered_uniform_space_dual : ordered_uniform_space → Type.
-intro; compose ordered_set_OF_ordered_uniform_space with os_r.
-apply (hos_carr (f o));
-qed.
 
-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.
@@ -114,24 +101,6 @@ lemma bs2_of_bss2:
 
 coercion bs2_of_bss2 nocomposites.
 
-(*
-notation < "x \sub \neq" with precedence 91 for @{'bsss $x}.
-interpretation "bs_of_ss" 'bsss x = (bs_of_ss _ _ _ x).
-*)
-
-(*
-lemma ss_of_bs: 
- ∀O:ordered_set.∀u,v:O.
-  ∀b:O squareO.\fst b ∈ [u,v] → \snd b ∈ [u,v] → {[u,v]} squareO ≝ 
- λO:ordered_set.λu,v:O.
-  λb:O squareB.λH1,H2.〈≪\fst b,H1≫,≪\snd b,H2≫〉.
-*)
-
-(*
-notation < "x \sub \nleq" with precedence 91 for @{'ssbs $x}.
-interpretation "ss_of_bs" 'ssbs x = (ss_of_bs _ _ _ x _ _).
-*)
-
 lemma segment_ordered_uniform_space: 
   ∀O:ordered_uniform_space.∀u,v:O.ordered_uniform_space.
 intros (O l r); apply mk_ordered_uniform_space;
@@ -185,16 +154,57 @@ 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:(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. 
+  ∀x:{[l,u]}.
+   ∀a:sequence {[l,u]}.
+    (⌊n, \fst (a n)⌋ : sequence O) uniform_converges (\fst x) → 
       a uniform_converges x.
 intros 8; cases H1; cases H2; clear H2 H1;
 cases (H ? H3) (m Hm); exists [apply m]; intros; 
 apply (restrict ? l u ??? H4); apply (Hm ? H1);
 qed.
 
+definition hint_sequence: 
+  ∀C:ordered_set.
+    sequence (hos_carr (os_l C)) → sequence (Type_of_ordered_set C).
+intros;assumption;
+qed.
+
+definition hint_sequence1: 
+  ∀C:ordered_set.
+    sequence (hos_carr (os_r C)) → sequence (Type_of_ordered_set_dual C).
+intros;assumption;
+qed.
+
+definition hint_sequence2: 
+  ∀C:ordered_set.
+    sequence (Type_of_ordered_set C) → sequence (hos_carr (os_l C)).
+intros;assumption;
+qed.
+
+definition hint_sequence3: 
+  ∀C:ordered_set.
+    sequence (Type_of_ordered_set_dual C) → sequence (hos_carr (os_r C)).
+intros;assumption;
+qed.
+
+coercion hint_sequence nocomposites.
+coercion hint_sequence1 nocomposites.
+coercion hint_sequence2 nocomposites.
+coercion hint_sequence3 nocomposites.
+
 definition order_continuity ≝
   λC:ordered_uniform_space.∀a:sequence C.∀x:C.
     (a ↑ x → a uniform_converges x) ∧ (a ↓ x → a uniform_converges x).
+
+lemma hint_boh1: ∀O. Type_OF_ordered_uniform_space O → hos_carr (os_l O).
+intros; assumption;
+qed.
+
+coercion hint_boh1 nocomposites. 
+
+lemma hint_boh2: ∀O:ordered_uniform_space. hos_carr (os_l O) → Type_OF_ordered_uniform_space O.
+intros; assumption;
+qed.
+
+coercion hint_boh2 nocomposites. 
+