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

diff --git a/helm/software/matita/contribs/dama/dama/lebesgue.ma b/helm/software/matita/contribs/dama/dama/lebesgue.ma
index af0a114534f74660564dfe7c05c204a947a71284..5740db8de5a980f06c254679301fcc0fd522e396 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/lebesgue.ma
+++ b/helm/software/matita/contribs/dama/dama/lebesgue.ma
@@ -38,7 +38,7 @@ cases (H3 j); clear H3; cases H2; cases H7; clear H2 H7;
 intro H2; cases (H10 ? H2);
 cases (H (w1+j)); apply (H11 H7);
 qed.   
-     
+          
 (* Theorem 3.10 *)
 theorem lebesgue_oc:
   ∀C:ordered_uniform_space.
@@ -47,8 +47,8 @@ theorem lebesgue_oc:
      ∀x:C.a order_converges x → 
       x ∈ [l,u] ∧ 
       ∀h:x ∈ [l,u].
-       uniform_converge {[l,u]} (â\8c\8an,â\8c©a n,H nâ\8cªâ\8c\8b) â\8c©x,hâ\8cª.
-intros;
+       uniform_converge {[l,u]} (â\8c\8an,â\89ªa n,H nâ\89«â\8c\8b) â\89ªx,hâ\89«.
+intros; 
 generalize in match (order_converges_bigger_lowsegment ???? H1 ? H2);
 generalize in match (order_converges_smaller_upsegment ???? H1 ? H2);
 cases H2 (xi yi Hx Hy Hxy); clear H2; simplify in ⊢ (% → % → ?); intros;
@@ -59,23 +59,23 @@ cut (∀i.xi i ∈ [l,u]) as Hxi; [2:
 cut (∀i.yi i ∈ [l,u]) as Hyi; [2:
   intros; split; [apply H2] cases (Hxy i) (_ H5); cases H5 (H7 _);
   apply (le_transitive ????? (H7 0)); simplify; 
-  cases (H1 i); assumption;] clear H2;
+  cases (H1 i); assumption;] clear H2; 
 split;
 [1: cases Hx; cases H3; cases Hy; cases H7; split;
     [1: apply (le_transitive ???? (H8 0)); cases (Hyi 0); assumption
     |2: apply (le_transitive ????? (H4 0)); cases (Hxi 0); assumption]
 |2: intros 3 (h);
-    letin Xi â\89\9d (â\8c\8an,â\8c©xi n,Hxi nâ\8cª⌋);
-    letin Yi â\89\9d (â\8c\8an,â\8c©yi n,Hyi nâ\8cª⌋);
-    letin Ai â\89\9d (â\8c\8an,â\8c©a n,H1 nâ\8cªâ\8c\8b);
-    apply (sandwich {[l,u]} â\8c©?,hâ\8cª Xi Yi Ai); try assumption;
+    letin Xi â\89\9d (â\8c\8an,â\89ªxi n, Hxi nâ\89«⌋);
+    letin Yi â\89\9d (â\8c\8an,â\89ªyi n, Hyi nâ\89«⌋);
+    letin Ai â\89\9d (â\8c\8an,â\89ªa n, H1 nâ\89«â\8c\8b); 
+    apply (sandwich {[l,u]} â\89ª?, hâ\89« Xi Yi Ai); [4: assumption;]
     [1: intro j; cases (Hxy j); cases H3; cases H4; split;
         [apply (H5 0);|apply (H7 0)]
-    |2: cases (H l u Xi â\8c©?,hâ\8cª) (Ux Uy); apply Ux; cases Hx; split; [apply H3;]
-        cases H4; split; [apply H5] intros (y Hy);cases (H6 (fst y));[2:apply Hy];
+    |2: cases (H l u Xi â\89ª?,hâ\89«) (Ux Uy); apply Ux; cases Hx; split; [apply H3;]
+        cases H4; split; [apply H5] intros (y Hy);cases (H6 (\fst y));[2:apply Hy];
         exists [apply w] apply H7; 
-    |3: cases (H l u Yi â\8c©?,hâ\8cª) (Ux Uy); apply Uy; cases Hy; split; [apply H3;]
-        cases H4; split; [apply H5] intros (y Hy);cases (H6 (fst y));[2:apply Hy];
+    |3: cases (H l u Yi â\89ª?,hâ\89«) (Ux Uy); apply Uy; cases Hy; split; [apply H3;]
+        cases H4; split; [apply H5] intros (y Hy);cases (H6 (\fst y));[2:apply Hy];
         exists [apply w] apply H7;]]
 qed.
  
@@ -88,7 +88,7 @@ theorem lebesgue_se:
      ∀x:C.a order_converges x → 
       x ∈ [l,u] ∧ 
       ∀h:x ∈ [l,u].
-       uniform_converge {[l,u]} (â\8c\8an,â\8c©a n,H nâ\8cªâ\8c\8b) â\8c©x,hâ\8cª.
+       uniform_converge {[l,u]} (â\8c\8an,â\89ªa n,H nâ\89«â\8c\8b) â\89ªx,hâ\89«.
 intros (C S);
 generalize in match (order_converges_bigger_lowsegment ???? H1 ? H2);
 generalize in match (order_converges_smaller_upsegment ???? H1 ? H2);
@@ -101,21 +101,18 @@ cut (∀i.yi i ∈ [l,u]) as Hyi; [2:
   intros; split; [apply H2] cases (Hxy i) (_ H5); cases H5 (H7 _);
   apply (le_transitive ????? (H7 0)); simplify; 
   cases (H1 i); assumption;] clear H2;
-split;
-[1: cases Hx; cases H3; cases Hy; cases H7; split;
-    [1: apply (le_transitive ???? (H8 0)); cases (Hyi 0); assumption
-    |2: apply (le_transitive ????? (H4 0)); cases (Hxi 0); assumption]
-|2: intros 3;
-    lapply (uparrow_upperlocated ? xi x Hx)as Ux;
-    lapply (downarrow_lowerlocated ? yi x Hy)as Uy;
-    letin Xi ≝ (⌊n,〈xi n,Hxi n〉⌋);
-    letin Yi ≝ (⌊n,〈yi n,Hyi n〉⌋);
-    letin Ai ≝ (⌊n,〈a n,H1 n〉⌋);
-    apply (sandwich {[l,u]} 〈x,h〉 Xi Yi Ai); try assumption;
-    [1: intro j; cases (Hxy j); cases H3; cases H4; split;
-        [apply (H5 0);|apply (H7 0)]
-    |2: cases (restrict_uniform_convergence_uparrow ? S ?? (H l u) Xi x Hx);
-        apply (H4 h);
-    |3: cases (restrict_uniform_convergence_downarrow ? S ?? (H l u) Yi x Hy);
-        apply (H4 h);]]
+letin Xi ≝ (⌊n,≪xi n, Hxi n≫⌋);
+letin Yi ≝ (⌊n,≪yi n, Hyi n≫⌋);
+cases (restrict_uniform_convergence_uparrow ? S ?? (H l u) Xi x Hx);
+cases (restrict_uniform_convergence_downarrow ? S ?? (H l u) Yi x Hy);
+split; [1: assumption]
+intros 3;
+lapply (uparrow_upperlocated ? xi x Hx)as Ux;
+lapply (downarrow_lowerlocated ? yi x Hy)as Uy;
+letin Ai ≝ (⌊n,≪a n, H1 n≫⌋);
+apply (sandwich {[l,u]} ≪?, h≫ Xi Yi Ai); [4: assumption;|2:apply H3;|3:apply H5]
+intro j; cases (Hxy j); cases H7; cases H8; split; [apply (H9 0);|apply (H11 0)]
 qed. 
+
+
+