--- a/src/HOL/List.thy Thu Feb 16 09:18:21 2012 +0100
+++ b/src/HOL/List.thy Thu Feb 16 09:18:23 2012 +0100
@@ -1801,7 +1801,7 @@
lemma drop_butlast: "drop n (butlast xs) = butlast (drop n xs)"
by (simp add: butlast_conv_take drop_take add_ac)
-lemma hd_drop_conv_nth: "\<lbrakk> xs \<noteq> []; n < length xs \<rbrakk> \<Longrightarrow> hd(drop n xs) = xs!n"
+lemma hd_drop_conv_nth: "n < length xs \<Longrightarrow> hd(drop n xs) = xs!n"
by(simp add: hd_conv_nth)
lemma set_take_subset_set_take:
@@ -2040,7 +2040,7 @@
done
lemma takeWhile_not_last:
- "\<lbrakk> xs \<noteq> []; distinct xs\<rbrakk> \<Longrightarrow> takeWhile (\<lambda>y. y \<noteq> last xs) xs = butlast xs"
+ "distinct xs \<Longrightarrow> takeWhile (\<lambda>y. y \<noteq> last xs) xs = butlast xs"
apply(induct xs)
apply simp
apply(case_tac xs)
@@ -2110,7 +2110,7 @@
by (induct xs ys rule:list_induct2') auto
lemma zip_append [simp]:
- "[| length xs = length us; length ys = length vs |] ==>
+ "[| length xs = length us |] ==>
zip (xs@ys) (us@vs) = zip xs us @ zip ys vs"
by (simp add: zip_append1)
@@ -3056,12 +3056,13 @@
by (induct xs) simp_all
lemma distinct_butlast:
- assumes "xs \<noteq> []" and "distinct xs"
+ assumes "distinct xs"
shows "distinct (butlast xs)"
-proof -
- from `xs \<noteq> []` obtain ys y where "xs = ys @ [y]" by (cases xs rule: rev_cases) auto
- with `distinct xs` show ?thesis by simp
-qed
+proof (cases "xs = []")
+ case False
+ from `xs \<noteq> []` obtain ys y where "xs = ys @ [y]" by (cases xs rule: rev_cases) auto
+ with `distinct xs` show ?thesis by simp
+qed (auto)
lemma remdups_map_remdups:
"remdups (map f (remdups xs)) = remdups (map f xs)"
@@ -3440,7 +3441,7 @@
lemma hd_replicate [simp]: "n \<noteq> 0 ==> hd (replicate n x) = x"
by (induct n) auto
-lemma tl_replicate [simp]: "n \<noteq> 0 ==> tl (replicate n x) = replicate (n - 1) x"
+lemma tl_replicate [simp]: "tl (replicate n x) = replicate (n - 1) x"
by (induct n) auto
lemma last_replicate [simp]: "n \<noteq> 0 ==> last (replicate n x) = x"