Most of the time, URIs can now be replaced with identifiers in "interpretation".

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

diff --git a/helm/software/matita/contribs/dama/dama/supremum.ma b/helm/software/matita/contribs/dama/dama/supremum.ma
index a3aa83d6af7d6bec3e5bb71ca0b112240cbf83d0..50b1ebedae5d64b9f1a8842fea85e20c440410af 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/supremum.ma
+++ b/helm/software/matita/contribs/dama/dama/supremum.ma
@@ -53,18 +53,12 @@ notation > "x 'is_supremum' s"  non associative with precedence 50
 notation > "x 'is_infimum' s"  non associative with precedence 50 
   for @{'infimum $s $x}.
 
-interpretation "Ordered set upper bound" 'upper_bound s x = 
-  (cic:/matita/dama/supremum/upper_bound.con _ s x).
-interpretation "Ordered set lower bound" 'lower_bound s x = 
-  (cic:/matita/dama/supremum/lower_bound.con _ s x).
-interpretation "Ordered set increasing"  'increasing s    = 
-  (cic:/matita/dama/supremum/increasing.con _ s).
-interpretation "Ordered set decreasing"  'decreasing s    = 
-  (cic:/matita/dama/supremum/decreasing.con _ s).
-interpretation "Ordered set strong sup"  'supremum s x  = 
-  (cic:/matita/dama/supremum/supremum.con _ s x).
-interpretation "Ordered set strong inf"  'infimum s x  = 
-  (cic:/matita/dama/supremum/infimum.con _ s x).
+interpretation "Ordered set upper bound" 'upper_bound s x = (upper_bound _ s x).
+interpretation "Ordered set lower bound" 'lower_bound s x = (lower_bound _ s x).
+interpretation "Ordered set increasing"  'increasing s    = (increasing _ s).
+interpretation "Ordered set decreasing"  'decreasing s    = (decreasing _ s).
+interpretation "Ordered set strong sup"  'supremum s x  = (supremum _ s x).
+interpretation "Ordered set strong inf"  'infimum s x  = (infimum _ s x).
   
 include "bishop_set.ma".
   
@@ -97,24 +91,24 @@ notation < "s \nbsp 'is_strictly_increasing'" non associative with precedence 50
 notation > "s 'is_strictly_increasing'" non associative with precedence 50 
   for @{'strictly_increasing $s}.
 interpretation "Ordered set strict increasing"  'strictly_increasing s    = 
-  (cic:/matita/dama/supremum/strictly_increasing.con _ s).
+  (strictly_increasing _ s).
 notation < "s \nbsp 'is_strictly_decreasing'" non associative with precedence 50 
   for @{'strictly_decreasing $s}.
 notation > "s 'is_strictly_decreasing'" non associative with precedence 50 
   for @{'strictly_decreasing $s}.
 interpretation "Ordered set strict decreasing"  'strictly_decreasing s    = 
-  (cic:/matita/dama/supremum/strictly_decreasing.con _ s).
+  (strictly_decreasing _ s).
   
 notation "a \uparrow u" non associative with precedence 50 for @{'sup_inc $a $u}.
 interpretation "Ordered set supremum of increasing" 'sup_inc s u =
  (cic:/matita/dama/cprop_connectives/And.ind#xpointer(1/1) 
-  (cic:/matita/dama/supremum/increasing.con _ s)
-  (cic:/matita/dama/supremum/supremum.con _ s u)).
+  (increasing _ s)
+  (supremum _ s u)).
 notation "a \downarrow u" non associative with precedence 50 for @{'inf_dec $a $u}.
 interpretation "Ordered set supremum of increasing" 'inf_dec s u =
  (cic:/matita/dama/cprop_connectives/And.ind#xpointer(1/1) 
-  (cic:/matita/dama/supremum/decreasing.con _ s)
-  (cic:/matita/dama/supremum/infimum.con _ s u)).
+  (decreasing _ s)
+  (infimum _ s u)).
 
 include "nat/plus.ma".
 include "nat_ordered_set.ma".
@@ -185,8 +179,7 @@ notation < "a \nbsp (\circ \atop (\horbar\triangleright)) \nbsp x" non associati
   for @{'order_converge $a $x}.
 notation > "a 'order_converges' x" non associative with precedence 50 
   for @{'order_converge $a $x}.
-interpretation "Order convergence" 'order_converge s u =
- (cic:/matita/dama/supremum/order_converge.con _ s u).   
+interpretation "Order convergence" 'order_converge s u = (order_converge _ s u).   
     
 (* Definition 2.8 *)
 
@@ -195,13 +188,11 @@ definition segment ≝ λO:ordered_set.λa,b:O.λx:O.
 
 notation "[a,b]" non associative with precedence 50 
   for @{'segment $a $b}.
-interpretation "Ordered set sergment" 'segment a b =
-  (cic:/matita/dama/supremum/segment.con _ a b).
+interpretation "Ordered set sergment" 'segment a b = (segment _ a b).
 
 notation "hvbox(x \in break [a,b])" non associative with precedence 50 
   for @{'segment2 $a $b $x}.
-interpretation "Ordered set sergment in" 'segment2 a b x=
-  (cic:/matita/dama/supremum/segment.con _ a b x).
+interpretation "Ordered set sergment in" 'segment2 a b x= (segment _ a b x).
 
 coinductive sigma (A:Type) (P:A→Prop) : Type ≝ sig_in : ∀x.P x → sigma A P.
 
@@ -211,8 +202,7 @@ notation < "'fst' \nbsp x" non associative with precedence 50 for @{'pi1 $x}.
 notation < "'snd' \nbsp x" non associative with precedence 50 for @{'pi2 $x}.
 notation > "'fst' x" non associative with precedence 50 for @{'pi1 $x}.
 notation > "'snd' x" non associative with precedence 50 for @{'pi2 $x}.
-interpretation "sigma pi1" 'pi1 x = 
- (cic:/matita/dama/supremum/pi1.con _ _ x).
+interpretation "sigma pi1" 'pi1 x = (pi1 _ _ x).
  
 interpretation "Type exists" 'exists \eta.x =
   (cic:/matita/dama/supremum/sigma.ind#xpointer(1/1) _ x).
@@ -228,7 +218,7 @@ qed.
 notation "hvbox({[a, break b]})" non associative with precedence 90 
   for @{'segment_set $a $b}.
 interpretation "Ordered set segment" 'segment_set a b = 
- (cic:/matita/dama/supremum/segment_ordered_set.con _ a b).
+ (segment_ordered_set _ a b).
 
 (* Lemma 2.9 *)
 lemma segment_preserves_supremum:
@@ -247,18 +237,14 @@ coinductive pair (A,B:Type) : Type ≝ prod : ∀a:A.∀b:B.pair A B.
 definition first : ∀A.∀P.pair A P → A ≝ λA,P,s.match s with [prod x _ ⇒ x].
 definition second : ∀A.∀P.pair A P → P ≝ λA,P,s.match s with [prod _ y ⇒ y].
   
-interpretation "pair pi1" 'pi1 x = 
- (cic:/matita/dama/supremum/first.con _ _ x).
-interpretation "pair pi2" 'pi2 x = 
- (cic:/matita/dama/supremum/second.con _ _ x).
+interpretation "pair pi1" 'pi1 x = (first _ _ x).
+interpretation "pair pi2" 'pi2 x = (second _ _ x).
 
 notation "hvbox(\langle a, break b\rangle)" non associative with precedence 91 for @{ 'pair $a $b}.
-interpretation "pair" 'pair a b = 
- (cic:/matita/dama/supremum/pair.ind#xpointer(1/1/1) _ _ a b).
+interpretation "pair" 'pair a b = (prod _ _ a b).
  
 notation "a \times b" left associative with precedence 60 for @{'prod $a $b}.
-interpretation "prod" 'prod a b = 
- (cic:/matita/dama/supremum/pair.ind#xpointer(1/1) a b).
+interpretation "prod" 'prod a b = (pair a b).
  
 lemma square_ordered_set: ordered_set → ordered_set.
 intro O; apply (mk_ordered_set (O × O));
@@ -275,8 +261,7 @@ notation < "s  2 \atop \nleq" non associative with precedence 90
   for @{ 'square $s }.
 notation > "s 'square'" non associative with precedence 90
   for @{ 'square $s }.
-interpretation "ordered set square" 'square s = 
- (cic:/matita/dama/supremum/square_ordered_set.con s).
+interpretation "ordered set square" 'square s = (square_ordered_set s).
  
 definition square_segment ≝ 
   λO:ordered_set.λa,b:O.λx:square_ordered_set O.
@@ -302,14 +287,14 @@ notation < "s \nbsp 'is_upper_located'" non associative with precedence 50
 notation > "s 'is_upper_located'" non associative with precedence 50 
   for @{'upper_located $s}.
 interpretation "Ordered set upper locatedness" 'upper_located s    = 
-  (cic:/matita/dama/supremum/upper_located.con _ s).
+  (upper_located _ s).
 
 notation < "s \nbsp 'is_lower_located'" non associative with precedence 50 
   for @{'lower_located $s}.
 notation > "s 'is_lower_located'" non associative with precedence 50 
   for @{'lower_located $s}.
 interpretation "Ordered set lower locatedness" 'lower_located s    = 
-  (cic:/matita/dama/supremum/lower_located.con _ s).
+  (lower_located _ s).
     
 (* Lemma 2.12 *)    
 lemma uparrow_upperlocated:
@@ -328,4 +313,4 @@ cases H3 (H4 H5); clear H3; cases (os_cotransitive ??? u Hxy) (W W);
 |2: right; exists [apply u]; split; [apply W|apply H4]]
 qed. 
      
-    
\ No newline at end of file
+