X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Fproperty_exhaustivity.ma;h=f7250f9e2e167a7a428b1d604c14638142580772;hb=910c252965fe17d6b5af92e4658e7d02bac82d58;hp=d04ec1acca886c457ae4370f3a5fcdc722120a9d;hpb=ca41435a6021292ccba239aa173651c0be705b45;p=helm.git

diff --git a/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma b/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
index d04ec1acc..f7250f9e2 100644
--- a/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
+++ b/helm/software/matita/contribs/dama/dama/property_exhaustivity.ma
@@ -34,7 +34,7 @@ qed.
 
 lemma segment_preserves_uparrow:
   ∀C:ordered_set.∀l,u:C.∀a:sequence {[l,u]}.∀x,h. 
-    ⌊n,\fst (a n)⌋ ↑ x → a ↑ 〈x,h〉.
+    ⌊n,\fst (a n)⌋ ↑ x → a ↑ ≪x,h≫.
 intros; cases H (Ha Hx); split [apply Ha] cases Hx; 
 split; [apply H1] intros;
 cases (H2 (\fst y)); [2: apply H3;] exists [apply w] assumption;
@@ -42,7 +42,7 @@ qed.
 
 lemma segment_preserves_downarrow:
   ∀C:ordered_set.∀l,u:C.∀a:sequence {[l,u]}.∀x,h. 
-    ⌊n,\fst (a n)⌋ ↓ x → a ↓ 〈x,h〉.
+    ⌊n,\fst (a n)⌋ ↓ x → a ↓ ≪x,h≫.
 intros; cases H (Ha Hx); split [apply Ha] cases Hx; 
 split; [apply H1] intros;
 cases (H2 (\fst y));[2:apply H3]; exists [apply w] assumption;
@@ -66,7 +66,7 @@ lemma restrict_uniform_convergence_uparrow:
   ∀C:ordered_uniform_space.property_sigma C →
     ∀l,u:C.exhaustive {[l,u]} →
      ∀a:sequence {[l,u]}.∀x:C. ⌊n,\fst (a n)⌋ ↑ x → 
-      x∈[l,u] ∧ ∀h:x ∈ [l,u].a uniform_converges 〈x,h〉.
+      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); 
@@ -74,9 +74,9 @@ intros; cases H2 (Ha Hx); clear H2; cases Hx; split;
     |2: apply (le_transitive ? ??? ? (H2 O));
         apply (segment_lowerbound ?l u);]
 |2: intros;
-    lapply (uparrow_upperlocated ? a 〈x,h〉) as Ha1;
+    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 (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;
@@ -88,7 +88,7 @@ lemma 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 → 
-      x∈[l,u] ∧ ∀h:x ∈ [l,u].a uniform_converges 〈x,h〉.
+      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); 
@@ -96,9 +96,9 @@ intros; cases H2 (Ha Hx); clear H2; cases Hx; split;
     |1: apply (le_transitive ???? (H2 O));
         apply (segment_upperbound ? l u);]
 |2: intros;
-    lapply (downarrow_lowerlocated ? a 〈x,h〉) as Ha1;
+    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 (segment_preserves_infimum ?l u 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;