more work on dama

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

diff --git a/helm/software/matita/contribs/dama/dama/uniform.ma b/helm/software/matita/contribs/dama/dama/uniform.ma
index faba6d83a68be9cc9f2e45d04b4a661072961b2b..82278eb08823e394bcfcbb23024f0e8206306175 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/uniform.ma
+++ b/helm/software/matita/contribs/dama/dama/uniform.ma
@@ -17,30 +17,28 @@ include "supremum.ma".
 
 (* Definition 2.13 *)
 alias symbol "square" = "bishop set square".
-alias symbol "pair" = "pair".
+alias symbol "pair" = "Pair construction".
 alias symbol "exists" = "exists".
 alias symbol "and" = "logical and".
 definition compose_bs_relations ≝
   λC:bishop_set.λU,V:C square → Prop.
-   λx:C square.∃y:C. U 〈fst x,y〉 ∧ V 〈y,snd x〉.
+   λx:C square.∃y:C. U 〈\fst x,y〉 ∧ V 〈y,\snd x〉.
    
 definition compose_os_relations ≝
   λC:ordered_set.λU,V:C square → Prop.
-   λx:C square.∃y:C. U 〈fst x,y〉 ∧ V 〈y,snd x〉.
+   λx:C square.∃y:C. U 〈\fst x,y〉 ∧ V 〈y,\snd x〉.
    
 interpretation "bishop set relations composition" 'compose a b = (compose_bs_relations _ a b).
 interpretation "ordered set relations composition" 'compose a b = (compose_os_relations _ a b).
 
 definition invert_bs_relation ≝
   λC:bishop_set.λU:C square → Prop.
-    λx:C square. U 〈snd x,fst x〉.
+    λx:C square. U 〈\snd x,\fst x〉.
     
-notation < "s \sup (-1)"  left associative with precedence 70
-  for @{ 'invert $s }.
-notation < "s \sup (-1) x"  left associative with precedence 70
+notation < "s \sup (-1)"  with precedence 70 for @{ 'invert $s }.
+notation < "s \sup (-1) x"  with precedence 70
   for @{ 'invert_appl $s $x}. 
-notation > "'inv'" right associative with precedence 70
-  for @{ 'invert_symbol  }.
+notation > "'inv'" with precedence 70 for @{ 'invert_symbol  }.
 interpretation "relation invertion" 'invert a = (invert_bs_relation _ a).
 interpretation "relation invertion" 'invert_symbol = (invert_bs_relation _).
 interpretation "relation invertion" 'invert_appl a x = (invert_bs_relation _ a x).
@@ -54,7 +52,7 @@ record uniform_space : Type ≝ {
   us_carr:> bishop_set;
   us_unifbase: (us_carr square → Prop) → CProp;
   us_phi1: ∀U:us_carr square → Prop. us_unifbase U → 
-    (λx:us_carr square.fst x ≈ snd x) ⊆ U;
+    (λx:us_carr square.\fst x ≈ \snd x) ⊆ U;
   us_phi2: ∀U,V:us_carr square → Prop. us_unifbase U → us_unifbase V →
     ∃W:us_carr square → Prop.us_unifbase W ∧ (W ⊆ (λx.U x ∧ V x));
   us_phi3: ∀U:us_carr square → Prop. us_unifbase U →