author bulwahn Thu, 16 Feb 2012 09:18:23 +0100 changeset 46500 0196966d6d2d parent 46499 ee996b8b0e5f child 46501 fe51817749d1
removing unnecessary premises in theorems of List theory
 src/HOL/List.thy file | annotate | diff | comparison | revisions
```--- 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)"

-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"

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"

@@ -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"```