src/HOL/Subst/AList.thy
changeset 24823 bfb619994060
parent 15635 8408a06590a6
child 38140 05691ad74079
--- a/src/HOL/Subst/AList.thy	Wed Oct 03 00:03:01 2007 +0200
+++ b/src/HOL/Subst/AList.thy	Wed Oct 03 19:36:05 2007 +0200
@@ -10,22 +10,19 @@
 imports Main
 begin
 
-consts
-  alist_rec  :: "[('a*'b)list, 'c, ['a, 'b, ('a*'b)list, 'c]=>'c] => 'c"
-  assoc      :: "['a,'b,('a*'b) list] => 'b"
-
+consts alist_rec  :: "[('a*'b)list, 'c, ['a, 'b, ('a*'b)list, 'c]=>'c] => 'c"
 primrec
   "alist_rec [] c d = c"
   "alist_rec (p # al) c d = d (fst p) (snd p) al (alist_rec al c d)"
 
+consts assoc      :: "['a,'b,('a*'b) list] => 'b"
 primrec
   "assoc v d [] = d"
   "assoc v d (p # al) = (if v = fst p then snd p else assoc v d al)"
 
-
 lemma alist_induct:
     "[| P([]);    
         !!x y xs. P(xs) ==> P((x,y)#xs) |]  ==> P(l)"
-by (induct_tac "l", auto)
+  by (induct l) auto
 
 end