X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdama%2Flebesgue.ma;h=cf96bf5b449ea5437f17064bda493452804b5415;hb=HEAD;hp=1b3f5025de55d3b50b8fed85c1f37f793c0db69c;hpb=c5a4db6c1020488d0792cee00dcf395a0ce54735;p=helm.git

diff --git a/helm/software/matita/library/dama/lebesgue.ma b/helm/software/matita/library/dama/lebesgue.ma
index 1b3f5025d..cf96bf5b4 100644
--- a/helm/software/matita/library/dama/lebesgue.ma
+++ b/helm/software/matita/library/dama/lebesgue.ma
@@ -22,11 +22,11 @@ lemma order_converges_bigger_lowsegment:
   ∀C:ordered_set.
    ∀a:sequence (os_l C).∀s:segment C.∀H:∀i:nat.a i ∈ s. 
      ∀x:C.∀p:order_converge C a x. 
-       ∀j. 𝕝_s ≤ (pi1exT23 ???? p j).
+       ∀j. 𝕝_ s ≤ (pi1exT23 ???? p j).
 intros; cases p (xi yi Ux Dy Hxy); clear p; simplify; 
 cases Ux (Ixi Sxi); clear Ux; cases Dy (Dyi Iyi); clear Dy;
 cases (Hxy j) (Ia Sa); clear Hxy; cases Ia (Da SSa); cases Sa (Inca SIa); clear Ia Sa;
-intro H2; cases (SSa 𝕝_s H2) (w Hw); simplify in Hw;
+intro H2; cases (SSa 𝕝_ s H2) (w Hw); simplify in Hw;
 lapply (H (w+j)) as K; cases (cases_in_segment ? s ? K); apply H3; apply Hw;
 qed.   
   
@@ -36,11 +36,11 @@ lemma order_converges_smaller_upsegment:
   ∀C:ordered_set.
    ∀a:sequence (os_l C).∀s:segment C.∀H:∀i:nat.a i ∈ s. 
      ∀x:C.∀p:order_converge C a x. 
-       ∀j. (pi2exT23 ???? p j) ≤ 𝕦_s.
+       ∀j. (pi2exT23 ???? p j) ≤ 𝕦_ s.
 intros; cases p (xi yi Ux Dy Hxy); clear p; simplify; 
 cases Ux (Ixi Sxi); clear Ux; cases Dy (Dyi Iyi); clear Dy;
 cases (Hxy j) (Ia Sa); clear Hxy; cases Ia (Da SSa); cases Sa (Inca SIa); clear Ia Sa;
-intro H2; cases (SIa 𝕦_s H2) (w Hw); lapply (H (w+j)) as K; 
+intro H2; cases (SIa 𝕦_ s H2) (w Hw); lapply (H (w+j)) as K; 
 cases (cases_in_segment ? s ? K); apply H1; apply Hw;  
 qed. 
 
@@ -60,11 +60,11 @@ cases H2 (xi yi Hx Hy Hxy); clear H2; simplify in ⊢ ((?→???%) → (?→???%)
 cut (∀i.xi i ∈ s) as Hxi; [2:
   intros; apply (prove_in_segment (os_l C)); [apply (H3 i)] cases (Hxy i) (H5 _); cases H5 (H7 _);
   lapply (H7 0) as K; cases (cases_in_segment ? s ? (H1 i)) (Pl Pu);
-  simplify in K:(? ? % ?); apply (hle_transitive (os_l C) (xi i) (a i) 𝕦_s K Pu);] clear H3;
+  simplify in K:(? ? % ?); apply (hle_transitive (os_l C) (xi i) (a i) 𝕦_ s K Pu);] clear H3;
 cut (∀i.yi i ∈ s) as Hyi; [2:
   intros; apply (prove_in_segment (os_l C)); [2:apply (H2 i)] cases (Hxy i) (_ H5); cases H5 (H7 _);
   lapply (H7 0) as K; cases (cases_in_segment ? s ? (H1 i)) (Pl Pu); simplify in K;
-  apply (le_transitive 𝕝_s ? ? ? K);apply Pl;] clear H2;
+  apply (le_transitive 𝕝_ s ? ? ? K);apply Pl;] clear H2;
 split;
 [1: apply (uparrow_to_in_segment s ? Hxi ? Hx);
 |2: intros 3 (h);
@@ -101,11 +101,11 @@ cases H2 (xi yi Hx Hy Hxy); clear H2; simplify in ⊢ ((?→???%) → (?→???%)
 cut (∀i.xi i ∈ s) as Hxi; [2:
   intros; apply (prove_in_segment (os_l C)); [apply (H3 i)] cases (Hxy i) (H5 _); cases H5 (H7 _);
   lapply (H7 0) as K; cases (cases_in_segment ? s ? (H1 i)) (Pl Pu);
-  simplify in K:(? ? % ?); apply (hle_transitive (os_l C) (xi i) (a i) 𝕦_s K Pu);] clear H3;
+  simplify in K:(? ? % ?); apply (hle_transitive (os_l C) (xi i) (a i) 𝕦_ s K Pu);] clear H3;
 cut (∀i.yi i ∈ s) as Hyi; [2:
   intros; apply (prove_in_segment (os_l C)); [2:apply (H2 i)] cases (Hxy i) (_ H5); cases H5 (H7 _);
   lapply (H7 0) as K; cases (cases_in_segment ? s ? (H1 i)) (Pl Pu); simplify in K;
-  apply (le_transitive 𝕝_s ? ? ? K);apply Pl;] clear H2;
+  apply (le_transitive 𝕝_ s ? ? ? K);apply Pl;] clear H2;
 letin Xi ≝ (⌊n,≪xi n, Hxi n≫⌋);
 letin Yi ≝ (⌊n,≪yi n, Hyi n≫⌋);
 cases (restrict_uniform_convergence_uparrow ? S ? (H s) Xi x Hx);