after a PITA, lebergue is dualized!

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

diff --git a/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma b/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
index f7250f9e2e167a7a428b1d604c14638142580772..96170fa262a6d25f553560e90bb76b5b3a11e5cb 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
+++ b/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
@@ -55,13 +55,13 @@ lemma segment_cauchy:
 intros 7; 
 alias symbol "pi1" (instance 3) = "pair pi1".
 alias symbol "pi2" = "pair pi2".
-apply (H (λx:{[l,u]} square.U 〈\fst (\fst x),\fst (\snd x)〉));
+apply (H (λx:{[l,u]} squareB.U 〈\fst (\fst x),\fst (\snd x)〉));
 (unfold segment_ordered_uniform_space; simplify);
 exists [apply U] split; [assumption;]
 intro; cases b; intros; simplify; split; intros; assumption;
 qed.       
 
-(* Lemma 3.8 *)
+(* Lemma 3.8 NON DUALIZZATO *)
 lemma restrict_uniform_convergence_uparrow:
   ∀C:ordered_uniform_space.property_sigma C →
     ∀l,u:C.exhaustive {[l,u]} →
@@ -69,39 +69,66 @@ lemma restrict_uniform_convergence_uparrow:
       x∈[l,u] ∧ ∀h:x ∈ [l,u].a uniform_converges ≪x,h≫.
 intros; cases H2 (Ha Hx); clear H2; cases Hx; split;
 [1: split;
-    [1: apply (supremum_is_upper_bound C ?? Hx u); 
+    [1: apply (supremum_is_upper_bound ? x Hx u); 
         apply (segment_upperbound ? l);
-    |2: apply (le_transitive ? ??? ? (H2 O));
-        apply (segment_lowerbound ?l u);]
+    |2: apply (le_transitive l ? x ? (H2 O));
+        apply (segment_lowerbound ? l u a 0);]
 |2: intros;
-    lapply (uparrow_upperlocated ? a ≪x,h≫) as Ha1;
-      [2: apply segment_preserves_uparrow;split; assumption;] 
-    lapply (segment_preserves_supremum ? l u a ≪?,h≫) as Ha2; 
+    lapply (uparrow_upperlocated a ≪x,h≫) as Ha1;
+      [2: apply (segment_preserves_uparrow C l u);split; assumption;] 
+    lapply (segment_preserves_supremum l u a ≪?,h≫) as Ha2; 
       [2:split; assumption]; cases Ha2; clear Ha2;
     cases (H1 a a); lapply (H6 H4 Ha1) as HaC;
     lapply (segment_cauchy ? l u ? HaC) as Ha;
     lapply (sigma_cauchy ? H  ? x ? Ha); [left; split; assumption]
     apply restric_uniform_convergence; assumption;]
 qed.
-      
-lemma restrict_uniform_convergence_downarrow:
+
+lemma hint_mah1:
+  ∀C. Type_OF_ordered_uniform_space1 C → hos_carr (os_r C).
+  intros; assumption; qed.
+  
+coercion hint_mah1 nocomposites.
+
+lemma hint_mah2:
+  ∀C. sequence (hos_carr (os_l C)) → sequence (hos_carr (os_r C)).
+  intros; assumption; qed.
+  
+coercion hint_mah2 nocomposites.
+
+lemma hint_mah3:
+  ∀C. Type_OF_ordered_uniform_space C → hos_carr (os_r C).
+  intros; assumption; qed.
+  
+coercion hint_mah3 nocomposites.
+    
+lemma hint_mah4:
+  ∀C. sequence (hos_carr (os_r C)) → sequence (hos_carr (os_l C)).
+  intros; assumption; qed.
+  
+coercion hint_mah4 nocomposites.
+
+axiom restrict_uniform_convergence_downarrow:
   ∀C:ordered_uniform_space.property_sigma C →
     ∀l,u:C.exhaustive {[l,u]} →
-     ∀a:sequence {[l,u]}.∀x:C. ⌊n,\fst (a n)⌋ ↓ x → 
+     ∀a:sequence {[l,u]}.∀x: C. ⌊n,\fst (a n)⌋ ↓ x → 
       x∈[l,u] ∧ ∀h:x ∈ [l,u].a uniform_converges ≪x,h≫.
+ (*
 intros; cases H2 (Ha Hx); clear H2; cases Hx; split;
 [1: split;
-    [2: apply (infimum_is_lower_bound C ?? Hx l); 
+    [2: apply (infimum_is_lower_bound ? x Hx l); 
         apply (segment_lowerbound ? l u);
-    |1: apply (le_transitive ???? (H2 O));
-        apply (segment_upperbound ? l u);]
+    |1: lapply (ge_transitive ? ? x ? (H2 O)); [apply u||assumption]
+        apply (segment_upperbound ? l u a 0);]
 |2: intros;
-    lapply (downarrow_lowerlocated ? a ≪x,h≫) as Ha1;
-      [2: apply segment_preserves_downarrow;split; assumption;] 
-    lapply (segment_preserves_infimum ?l u a ≪?,h≫) as Ha2; 
+    lapply (downarrow_lowerlocated a ≪x,h≫) as Ha1;
+      [2: apply (segment_preserves_downarrow ? l u);split; assumption;] 
+    lapply (segment_preserves_infimum l u); 
+      [2: apply a; ≪?,h≫) as Ha2; 
       [2:split; assumption]; cases Ha2; clear Ha2;
     cases (H1 a a); lapply (H7 H4 Ha1) as HaC;
     lapply (segment_cauchy ? l u ? HaC) as Ha;
     lapply (sigma_cauchy ? H  ? x ? Ha); [right; split; assumption]
     apply restric_uniform_convergence; assumption;]
-qed.
\ No newline at end of file
+qed.
+*)
\ No newline at end of file