X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Flist%2Flist.ma;h=d5664f4166c783914af3be60f1d60bc25a008a79;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=417c88ee78acbacfde334c794d3b60293a95199a;hpb=ba1543704989d6d60f1e510b5957368957dc519e;p=helm.git

diff --git a/helm/matita/library/list/list.ma b/helm/matita/library/list/list.ma
index 417c88ee7..d5664f416 100644
--- a/helm/matita/library/list/list.ma
+++ b/helm/matita/library/list/list.ma
@@ -16,9 +16,6 @@ set "baseuri" "cic:/matita/list/".
 include "logic/equality.ma".
 include "higher_order_defs/functions.ma".
 
-interpretation "leibnitz's equality" 'eq x y =
-  (cic:/matita/logic/equality/eq.ind#xpointer(1/1) _ x y).
-
 notation "hvbox(hd break :: tl)"
   right associative with precedence 46
   for @{'cons $hd $tl}.
@@ -31,31 +28,38 @@ notation "hvbox(l1 break @ l2)"
   right associative with precedence 47
   for @{'append $l1 $l2 }.
 
-inductive list (A:Set) : Set \def
+inductive list (A:Set) : Set :=
   | nil: list A
-  | cons: A \to list A \to list A.
+  | cons: A -> list A -> list A.
 
 interpretation "nil" 'nil = (cic:/matita/list/list.ind#xpointer(1/1/1) _).
 interpretation "cons" 'cons hd tl =
   (cic:/matita/list/list.ind#xpointer(1/1/2) _ hd tl).
 
+(* theorem test_notation: [O; S O; S (S O)] = O :: S O :: S (S O) :: []. *)
+
 theorem nil_cons:
   \forall A:Set.\forall l:list A.\forall a:A.
-    a::l \neq [].
+    a::l <> [].
   intros.
   unfold; intros.
   discriminate H.
 qed.
 
-let rec id_list A (l: list A) on l \def
+let rec id_list A (l: list A) on l :=
   match l with
-  [ nil \Rightarrow []
-  | (cons hd tl) \Rightarrow hd :: id_list A tl ].
+  [ nil => []
+  | (cons hd tl) => hd :: id_list A tl ].
 
-let rec append A (l1: list A) l2 on l1 \def
+let rec append A (l1: list A) l2 on l1 :=
   match l1 with
-  [ nil \Rightarrow l2
-  | (cons hd tl) \Rightarrow hd :: append A tl l2 ].
+  [ nil => l2
+  | (cons hd tl) => hd :: append A tl l2 ].
+
+definition tail := \lambda A:Set. \lambda l: list A.
+  match l with
+  [ nil => []
+  | (cons hd tl) => tl].
 
 interpretation "append" 'append l1 l2 = (cic:/matita/list/append.con _ l1 l2).