X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Flist%2Flist.ma;h=ffa2c8ef9ac106c007f701cef1cf21b589f51a19;hb=112afe13b5aef27425d1a0bc9c71a70b491069bf;hp=0b7340d051ce5fc1f34e4f5480bea986df6c5247;hpb=2826aed999b30a6f53978fe457c1e5f3587ac6d6;p=helm.git

diff --git a/helm/matita/library/list/list.ma b/helm/matita/library/list/list.ma
index 0b7340d05..ffa2c8ef9 100644
--- a/helm/matita/library/list/list.ma
+++ b/helm/matita/library/list/list.ma
@@ -16,6 +16,10 @@ set "baseuri" "cic:/matita/list/".
 include "logic/equality.ma".
 include "higher_order_defs/functions.ma".
 
+inductive list (A:Set) : Set :=
+  | nil: list A
+  | cons: A -> list A -> list A.
+
 notation "hvbox(hd break :: tl)"
   right associative with precedence 46
   for @{'cons $hd $tl}.
@@ -28,57 +32,64 @@ notation "hvbox(l1 break @ l2)"
   right associative with precedence 47
   for @{'append $l1 $l2 }.
 
-inductive list (A:Set) : Set \def
-  | nil: list A
-  | cons: A \to list A \to 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 [].
-  intros.
-  unfold; intros.
+    a::l <> [].
+  intros;
+  unfold Not;
+  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).
 
 theorem append_nil: \forall A:Set.\forall l:list A.l @ [] = l.
-  intros.
-  elim l.
-  reflexivity.
-  simplify.
-  rewrite > H.
-  reflexivity.
+  intros;
+  elim l;
+  [ reflexivity;
+  | simplify;
+    rewrite > H;
+    reflexivity;
+  ]
 qed.
 
 theorem associative_append: \forall A:Set.associative (list A) (append A).
-  intros; unfold; intros.
-  elim x.
-  simplify; reflexivity.
-  simplify.
-  rewrite > H.
-  reflexivity.
+  intros; unfold; intros;
+  elim x;
+  [ simplify;
+    reflexivity;
+  | simplify;
+    rewrite > H;
+    reflexivity;
+  ]
 qed.
 
 theorem cons_append_commute:
   \forall A:Set.\forall l1,l2:list A.\forall a:A.
     a :: (l1 @ l2) = (a :: l1) @ l2.
-  intros.
-  reflexivity.
+  intros;
+  reflexivity;
 qed.
 
 (*