some work on duality, still not finisched

[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 ed9e6fe5d1d60a66ddf205d8e1bbcbe7f0ffd113..759037124310076d813c711ea272eb323d2d6ffc 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/uniform.ma
+++ b/helm/software/matita/contribs/dama/dama/uniform.ma
@@ -14,31 +14,26 @@
 
 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〉.
+  λC:bishop_set.λU,V:C squareB → Prop.
+   λx:C squareB.∃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〉.
+  λC:ordered_set.λU,V:C squareB → Prop.
+   λx:C squareB.∃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〉.
-    
-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'" with precedence 70 for @{ 'invert_symbol  }.
+  λC:bishop_set.λU:C squareB → Prop.
+    λx:C squareB. U 〈\snd x,\fst x〉.
+      
+notation > "\inv" with precedence 60 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).
@@ -50,14 +45,14 @@ alias symbol "and" (instance 16) = "constructive and".
 alias symbol "and" (instance 9) = "constructive and".
 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;
-  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 → 
-    ∃W:us_carr square → Prop.us_unifbase W ∧ (W ∘ W) ⊆ U;
-  us_phi4: ∀U:us_carr square → Prop. us_unifbase U → ∀x.(U x → (inv U) x) ∧ ((inv U) x → U x)
+  us_unifbase: (us_carr squareB → Prop) → CProp;
+  us_phi1: ∀U:us_carr squareB → Prop. us_unifbase U → 
+    (λx:us_carr squareB.\fst x ≈ \snd x) ⊆ U;
+  us_phi2: ∀U,V:us_carr squareB → Prop. us_unifbase U → us_unifbase V →
+    ∃W:us_carr squareB → Prop.us_unifbase W ∧ (W ⊆ (λx.U x ∧ V x));
+  us_phi3: ∀U:us_carr squareB → Prop. us_unifbase U → 
+    ∃W:us_carr squareB → Prop.us_unifbase W ∧ (W ∘ W) ⊆ U;
+  us_phi4: ∀U:us_carr squareB → Prop. us_unifbase U → ∀x.(U x → (\inv U) x) ∧ ((\inv U) x → U x)
 }.
 
 (* Definition 2.14 *)  
@@ -66,9 +61,9 @@ definition cauchy ≝
   λC:uniform_space.λa:sequence C.∀U.us_unifbase C U → 
    ∃n. ∀i,j. n ≤ i → n ≤ j → U 〈a i,a j〉.
    
-notation < "a \nbsp 'is_cauchy'" non associative with precedence 50 
+notation < "a \nbsp 'is_cauchy'" non associative with precedence 45 
   for @{'cauchy $a}.
-notation > "a 'is_cauchy'" non associative with precedence 50 
+notation > "a 'is_cauchy'" non associative with precedence 45 
   for @{'cauchy $a}.
 interpretation "Cauchy sequence" 'cauchy s = (cauchy _ s).  
    
@@ -77,9 +72,9 @@ definition uniform_converge ≝
   λC:uniform_space.λa:sequence C.λu:C.
     ∀U.us_unifbase C U →  ∃n. ∀i. n ≤ i → U 〈u,a i〉.
     
-notation < "a \nbsp (\u \atop (\horbar\triangleright)) \nbsp x" non associative with precedence 50 
+notation < "a \nbsp (\u \atop (\horbar\triangleright)) \nbsp x" non associative with precedence 45 
   for @{'uniform_converge $a $x}.
-notation > "a 'uniform_converges' x" non associative with precedence 50 
+notation > "a 'uniform_converges' x" non associative with precedence 45 
   for @{'uniform_converge $a $x}.
 interpretation "Uniform convergence" 'uniform_converge s u =
  (uniform_converge _ s u).