Using Prop conjuction on Props lowers the universes.

[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..6daebfa0cde944051d1b03fe7d2ddd35cd415d3e 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.
@@ -47,7 +47,7 @@ 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.
+       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);
@@ -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,mk_sigT ?? (xi n) (Hxi n)⌋);
+    letin Yi ≝ (⌊n,mk_sigT ?? (yi n) (Hyi n)⌋);
+    letin Ai ≝ (⌊n,mk_sigT ?? (a n) (H1 n)⌋);
+    apply (sandwich {[l,u]} (mk_sigT ?? 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 (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);
@@ -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,mk_sigT ?? (xi n) (Hxi n)⌋);
+    letin Yi ≝ (⌊n,mk_sigT ?? (yi n) (Hyi n)⌋);
+    letin Ai ≝ (⌊n,mk_sigT ?? (a n) (H1 n)⌋);
+    apply (sandwich {[l,u]} (mk_sigT ?? 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);