X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Flebesgue.ma;h=e1fbd0a5a75cac9f840d207833e3319214680224;hb=d97f69b313893900ca2d57544fcd200eb06ee286;hp=af0a114534f74660564dfe7c05c204a947a71284;hpb=cb2419357a3f80388f71eb2730bff154bd4ef000;p=helm.git

diff --git a/helm/software/matita/contribs/dama/dama/lebesgue.ma b/helm/software/matita/contribs/dama/dama/lebesgue.ma
index af0a11453..e1fbd0a5a 100644
--- a/helm/software/matita/contribs/dama/dama/lebesgue.ma
+++ b/helm/software/matita/contribs/dama/dama/lebesgue.ma
@@ -47,7 +47,7 @@ theorem lebesgue_oc:
      ∀x:C.a order_converges x → 
       x ∈ [l,u] ∧ 
       ∀h:x ∈ [l,u].
-       uniform_converge {[l,u]} (⌊n,〈a n,H n〉⌋) 〈x,h〉.
+       uniform_converge {[l,u]} (⌊n,≪a n,H n≫⌋) ≪x,h≫.
 intros;
 generalize in match (order_converges_bigger_lowsegment ???? H1 ? H2);
 generalize in match (order_converges_smaller_upsegment ???? H1 ? H2);
@@ -65,17 +65,17 @@ 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 ≝ (⌊n,〈xi n,Hxi n〉⌋);
-    letin Yi ≝ (⌊n,〈yi n,Hyi n〉⌋);
-    letin Ai ≝ (⌊n,〈a n,H1 n〉⌋);
-    apply (sandwich {[l,u]} 〈?,h〉 Xi Yi Ai); try assumption;
+    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]} ≪?,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 (H l u Xi 〈?,h〉) (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 ≪?,h≫) (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 〈?,h〉) (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 ≪?,h≫) (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]} (⌊n,〈a n,H n〉⌋) 〈x,h〉.
+       uniform_converge {[l,u]} (⌊n,≪a n,H n≫⌋) ≪x,h≫.
 intros (C S);
 generalize in match (order_converges_bigger_lowsegment ???? H1 ? H2);
 generalize in match (order_converges_smaller_upsegment ???? H1 ? H2);
@@ -108,10 +108,10 @@ split;
 |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;
+    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);