diff --git a/src/HOL/Library/More_List.thy b/src/HOL/Library/More_List.thy
--- a/src/HOL/Library/More_List.thy
+++ b/src/HOL/Library/More_List.thy
@@ -1,395 +1,395 @@
 (* Author: Andreas Lochbihler, ETH Zürich
    Author: Florian Haftmann, TU Muenchen  *)
 
 section \<open>Less common functions on lists\<close>
 
 theory More_List
 imports Main
 begin
 
 definition strip_while :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> 'a list"
 where
   "strip_while P = rev \<circ> dropWhile P \<circ> rev"
 
 lemma strip_while_rev [simp]:
   "strip_while P (rev xs) = rev (dropWhile P xs)"
   by (simp add: strip_while_def)
   
 lemma strip_while_Nil [simp]:
   "strip_while P [] = []"
   by (simp add: strip_while_def)
 
 lemma strip_while_append [simp]:
   "\<not> P x \<Longrightarrow> strip_while P (xs @ [x]) = xs @ [x]"
   by (simp add: strip_while_def)
 
 lemma strip_while_append_rec [simp]:
   "P x \<Longrightarrow> strip_while P (xs @ [x]) = strip_while P xs"
   by (simp add: strip_while_def)
 
 lemma strip_while_Cons [simp]:
   "\<not> P x \<Longrightarrow> strip_while P (x # xs) = x # strip_while P xs"
   by (induct xs rule: rev_induct) (simp_all add: strip_while_def)
 
 lemma strip_while_eq_Nil [simp]:
   "strip_while P xs = [] \<longleftrightarrow> (\<forall>x\<in>set xs. P x)"
   by (simp add: strip_while_def)
 
 lemma strip_while_eq_Cons_rec:
   "strip_while P (x # xs) = x # strip_while P xs \<longleftrightarrow> \<not> (P x \<and> (\<forall>x\<in>set xs. P x))"
   by (induct xs rule: rev_induct) (simp_all add: strip_while_def)
 
 lemma split_strip_while_append:
   fixes xs :: "'a list"
   obtains ys zs :: "'a list"
   where "strip_while P xs = ys" and "\<forall>x\<in>set zs. P x" and "xs = ys @ zs"
 proof (rule that)
   show "strip_while P xs = strip_while P xs" ..
   show "\<forall>x\<in>set (rev (takeWhile P (rev xs))). P x" by (simp add: takeWhile_eq_all_conv [symmetric])
   have "rev xs = rev (strip_while P xs @ rev (takeWhile P (rev xs)))"
     by (simp add: strip_while_def)
   then show "xs = strip_while P xs @ rev (takeWhile P (rev xs))"
     by (simp only: rev_is_rev_conv)
 qed
 
 lemma strip_while_snoc [simp]:
   "strip_while P (xs @ [x]) = (if P x then strip_while P xs else xs @ [x])"
   by (simp add: strip_while_def)
 
 lemma strip_while_map:
   "strip_while P (map f xs) = map f (strip_while (P \<circ> f) xs)"
   by (simp add: strip_while_def rev_map dropWhile_map)
 
 lemma strip_while_dropWhile_commute:
   "strip_while P (dropWhile Q xs) = dropWhile Q (strip_while P xs)"
 proof (induct xs)
   case Nil
   then show ?case
     by simp
 next
   case (Cons x xs)
   show ?case
   proof (cases "\<forall>y\<in>set xs. P y")
     case True
     with dropWhile_append2 [of "rev xs"] show ?thesis
       by (auto simp add: strip_while_def dest: set_dropWhileD)
   next
     case False
     then obtain y where "y \<in> set xs" and "\<not> P y"
       by blast
     with Cons dropWhile_append3 [of P y "rev xs"] show ?thesis
       by (simp add: strip_while_def)
   qed
 qed
 
 lemma dropWhile_strip_while_commute:
   "dropWhile P (strip_while Q xs) = strip_while Q (dropWhile P xs)"
   by (simp add: strip_while_dropWhile_commute)
 
 
 definition no_leading :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool"
 where
   "no_leading P xs \<longleftrightarrow> (xs \<noteq> [] \<longrightarrow> \<not> P (hd xs))"
 
-lemma no_leading_Nil [simp, intro!]:
+lemma no_leading_Nil [iff]:
   "no_leading P []"
   by (simp add: no_leading_def)
 
-lemma no_leading_Cons [simp, intro!]:
+lemma no_leading_Cons [iff]:
   "no_leading P (x # xs) \<longleftrightarrow> \<not> P x"
   by (simp add: no_leading_def)
 
 lemma no_leading_append [simp]:
   "no_leading P (xs @ ys) \<longleftrightarrow> no_leading P xs \<and> (xs = [] \<longrightarrow> no_leading P ys)"
   by (induct xs) simp_all
 
 lemma no_leading_dropWhile [simp]:
   "no_leading P (dropWhile P xs)"
   by (induct xs) simp_all
 
 lemma dropWhile_eq_obtain_leading:
   assumes "dropWhile P xs = ys"
   obtains zs where "xs = zs @ ys" and "\<And>z. z \<in> set zs \<Longrightarrow> P z" and "no_leading P ys"
 proof -
   from assms have "\<exists>zs. xs = zs @ ys \<and> (\<forall>z \<in> set zs. P z) \<and> no_leading P ys"
   proof (induct xs arbitrary: ys)
     case Nil then show ?case by simp
   next
     case (Cons x xs ys)
     show ?case proof (cases "P x")
       case True with Cons.hyps [of ys] Cons.prems
       have "\<exists>zs. xs = zs @ ys \<and> (\<forall>a\<in>set zs. P a) \<and> no_leading P ys"
         by simp
       then obtain zs where "xs = zs @ ys" and "\<And>z. z \<in> set zs \<Longrightarrow> P z"
         and *: "no_leading P ys"
         by blast
       with True have "x # xs = (x # zs) @ ys" and "\<And>z. z \<in> set (x # zs) \<Longrightarrow> P z"
         by auto
       with * show ?thesis
         by blast    next
       case False
       with Cons show ?thesis by (cases ys) simp_all
     qed
   qed
   with that show thesis
     by blast
 qed
 
 lemma dropWhile_idem_iff:
   "dropWhile P xs = xs \<longleftrightarrow> no_leading P xs"
   by (cases xs) (auto elim: dropWhile_eq_obtain_leading)
 
 
 abbreviation no_trailing :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool"
 where
   "no_trailing P xs \<equiv> no_leading P (rev xs)"
 
 lemma no_trailing_unfold:
   "no_trailing P xs \<longleftrightarrow> (xs \<noteq> [] \<longrightarrow> \<not> P (last xs))"
   by (induct xs) simp_all
 
-lemma no_trailing_Nil [simp, intro!]:
+lemma no_trailing_Nil [iff]:
   "no_trailing P []"
   by simp
 
 lemma no_trailing_Cons [simp]:
   "no_trailing P (x # xs) \<longleftrightarrow> no_trailing P xs \<and> (xs = [] \<longrightarrow> \<not> P x)"
   by simp
 
 lemma no_trailing_append:
   "no_trailing P (xs @ ys) \<longleftrightarrow> no_trailing P ys \<and> (ys = [] \<longrightarrow> no_trailing P xs)"
   by (induct xs) simp_all
 
 lemma no_trailing_append_Cons [simp]:
   "no_trailing P (xs @ y # ys) \<longleftrightarrow> no_trailing P (y # ys)"
   by simp
 
 lemma no_trailing_strip_while [simp]:
   "no_trailing P (strip_while P xs)"
   by (induct xs rule: rev_induct) simp_all
 
 lemma strip_while_idem [simp]:
   "no_trailing P xs \<Longrightarrow> strip_while P xs = xs"
   by (cases xs rule: rev_cases) simp_all
 
 lemma strip_while_eq_obtain_trailing:
   assumes "strip_while P xs = ys"
   obtains zs where "xs = ys @ zs" and "\<And>z. z \<in> set zs \<Longrightarrow> P z" and "no_trailing P ys"
 proof -
   from assms have "rev (rev (dropWhile P (rev xs))) = rev ys"
     by (simp add: strip_while_def)
   then have "dropWhile P (rev xs) = rev ys"
     by simp
   then obtain zs where A: "rev xs = zs @ rev ys" and B: "\<And>z. z \<in> set zs \<Longrightarrow> P z"
     and C: "no_trailing P ys"
     using dropWhile_eq_obtain_leading by blast
   from A have "rev (rev xs) = rev (zs @ rev ys)"
     by simp
   then have "xs = ys @ rev zs"
     by simp
   moreover from B have "\<And>z. z \<in> set (rev zs) \<Longrightarrow> P z"
     by simp
   ultimately show thesis using that C by blast
 qed
 
 lemma strip_while_idem_iff:
   "strip_while P xs = xs \<longleftrightarrow> no_trailing P xs"
 proof -
   define ys where "ys = rev xs"
   moreover have "strip_while P (rev ys) = rev ys \<longleftrightarrow> no_trailing P (rev ys)"
     by (simp add: dropWhile_idem_iff)
   ultimately show ?thesis by simp
 qed
 
 lemma no_trailing_map:
   "no_trailing P (map f xs) \<longleftrightarrow> no_trailing (P \<circ> f) xs"
   by (simp add: last_map no_trailing_unfold)
 
 lemma no_trailing_drop [simp]:
   "no_trailing P (drop n xs)" if "no_trailing P xs"
 proof -
   from that have "no_trailing P (take n xs @ drop n xs)"
     by simp
   then show ?thesis
     by (simp only: no_trailing_append)
 qed
 
 lemma no_trailing_upt [simp]:
   "no_trailing P [n..<m] \<longleftrightarrow> (n < m \<longrightarrow> \<not> P (m - 1))"
   by (auto simp add: no_trailing_unfold)
 
 
 definition nth_default :: "'a \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow> 'a"
 where
   "nth_default dflt xs n = (if n < length xs then xs ! n else dflt)"
 
 lemma nth_default_nth:
   "n < length xs \<Longrightarrow> nth_default dflt xs n = xs ! n"
   by (simp add: nth_default_def)
 
 lemma nth_default_beyond:
   "length xs \<le> n \<Longrightarrow> nth_default dflt xs n = dflt"
   by (simp add: nth_default_def)
 
 lemma nth_default_Nil [simp]:
   "nth_default dflt [] n = dflt"
   by (simp add: nth_default_def)
 
 lemma nth_default_Cons:
   "nth_default dflt (x # xs) n = (case n of 0 \<Rightarrow> x | Suc n' \<Rightarrow> nth_default dflt xs n')"
   by (simp add: nth_default_def split: nat.split)
 
 lemma nth_default_Cons_0 [simp]:
   "nth_default dflt (x # xs) 0 = x"
   by (simp add: nth_default_Cons)
 
 lemma nth_default_Cons_Suc [simp]:
   "nth_default dflt (x # xs) (Suc n) = nth_default dflt xs n"
   by (simp add: nth_default_Cons)
 
 lemma nth_default_replicate_dflt [simp]:
   "nth_default dflt (replicate n dflt) m = dflt"
   by (simp add: nth_default_def)
 
 lemma nth_default_append:
   "nth_default dflt (xs @ ys) n =
     (if n < length xs then nth xs n else nth_default dflt ys (n - length xs))"
   by (auto simp add: nth_default_def nth_append)
 
 lemma nth_default_append_trailing [simp]:
   "nth_default dflt (xs @ replicate n dflt) = nth_default dflt xs"
   by (simp add: fun_eq_iff nth_default_append) (simp add: nth_default_def)
 
 lemma nth_default_snoc_default [simp]:
   "nth_default dflt (xs @ [dflt]) = nth_default dflt xs"
   by (auto simp add: nth_default_def fun_eq_iff nth_append)
 
 lemma nth_default_eq_dflt_iff:
   "nth_default dflt xs k = dflt \<longleftrightarrow> (k < length xs \<longrightarrow> xs ! k = dflt)"
   by (simp add: nth_default_def)
 
 lemma nth_default_take_eq:
   "nth_default dflt (take m xs) n =
     (if n < m then nth_default dflt xs n else dflt)"
   by (simp add: nth_default_def)
 
 lemma in_enumerate_iff_nth_default_eq:
   "x \<noteq> dflt \<Longrightarrow> (n, x) \<in> set (enumerate 0 xs) \<longleftrightarrow> nth_default dflt xs n = x"
   by (auto simp add: nth_default_def in_set_conv_nth enumerate_eq_zip)
 
 lemma last_conv_nth_default:
   assumes "xs \<noteq> []"
   shows "last xs = nth_default dflt xs (length xs - 1)"
   using assms by (simp add: nth_default_def last_conv_nth)
   
 lemma nth_default_map_eq:
   "f dflt' = dflt \<Longrightarrow> nth_default dflt (map f xs) n = f (nth_default dflt' xs n)"
   by (simp add: nth_default_def)
 
 lemma finite_nth_default_neq_default [simp]:
   "finite {k. nth_default dflt xs k \<noteq> dflt}"
   by (simp add: nth_default_def)
 
 lemma sorted_list_of_set_nth_default:
   "sorted_list_of_set {k. nth_default dflt xs k \<noteq> dflt} = map fst (filter (\<lambda>(_, x). x \<noteq> dflt) (enumerate 0 xs))"
   by (rule sorted_distinct_set_unique) (auto simp add: nth_default_def in_set_conv_nth
     sorted_filter distinct_map_filter enumerate_eq_zip intro: rev_image_eqI)
 
 lemma map_nth_default:
   "map (nth_default x xs) [0..<length xs] = xs"
 proof -
   have *: "map (nth_default x xs) [0..<length xs] = map (List.nth xs) [0..<length xs]"
     by (rule map_cong) (simp_all add: nth_default_nth)
   show ?thesis by (simp add: * map_nth)
 qed
 
 lemma range_nth_default [simp]:
   "range (nth_default dflt xs) = insert dflt (set xs)"
   by (auto simp add: nth_default_def [abs_def] in_set_conv_nth)
 
 lemma nth_strip_while:
   assumes "n < length (strip_while P xs)"
   shows "strip_while P xs ! n = xs ! n"
 proof -
   have "length (dropWhile P (rev xs)) + length (takeWhile P (rev xs)) = length xs"
     by (subst add.commute)
       (simp add: arg_cong [where f=length, OF takeWhile_dropWhile_id, unfolded length_append])
   then show ?thesis using assms
     by (simp add: strip_while_def rev_nth dropWhile_nth)
 qed
 
 lemma length_strip_while_le:
   "length (strip_while P xs) \<le> length xs"
   unfolding strip_while_def o_def length_rev
   by (subst (2) length_rev[symmetric])
     (simp add: strip_while_def length_dropWhile_le del: length_rev)
 
 lemma nth_default_strip_while_dflt [simp]:
   "nth_default dflt (strip_while ((=) dflt) xs) = nth_default dflt xs"
   by (induct xs rule: rev_induct) auto
 
 lemma nth_default_eq_iff:
   "nth_default dflt xs = nth_default dflt ys
      \<longleftrightarrow> strip_while (HOL.eq dflt) xs = strip_while (HOL.eq dflt) ys" (is "?P \<longleftrightarrow> ?Q")
 proof
   let ?xs = "strip_while (HOL.eq dflt) xs" and ?ys = "strip_while (HOL.eq dflt) ys"
   assume ?P
   then have eq: "nth_default dflt ?xs = nth_default dflt ?ys"
     by simp
   have len: "length ?xs = length ?ys"
   proof (rule ccontr)
     assume len: "length ?xs \<noteq> length ?ys"
     { fix xs ys :: "'a list"
       let ?xs = "strip_while (HOL.eq dflt) xs" and ?ys = "strip_while (HOL.eq dflt) ys"
       assume eq: "nth_default dflt ?xs = nth_default dflt ?ys"
       assume len: "length ?xs < length ?ys"
       then have "length ?ys > 0" by arith
       then have "?ys \<noteq> []" by simp
       with last_conv_nth_default [of ?ys dflt]
       have "last ?ys = nth_default dflt ?ys (length ?ys - 1)"
         by auto
       moreover from \<open>?ys \<noteq> []\<close> no_trailing_strip_while [of "HOL.eq dflt" ys]
         have "last ?ys \<noteq> dflt" by (simp add: no_trailing_unfold)
       ultimately have "nth_default dflt ?xs (length ?ys - 1) \<noteq> dflt"
         using eq by simp
       moreover from len have "length ?ys - 1 \<ge> length ?xs" by simp
       ultimately have False by (simp only: nth_default_beyond) simp
     } 
     from this [of xs ys] this [of ys xs] len eq show False
       by (auto simp only: linorder_class.neq_iff)
   qed
   then show ?Q
   proof (rule nth_equalityI [rule_format])
     fix n
     assume n: "n < length ?xs"
     with len have "n < length ?ys"
       by simp
     with n have xs: "nth_default dflt ?xs n = ?xs ! n"
       and ys: "nth_default dflt ?ys n = ?ys ! n"
       by (simp_all only: nth_default_nth)
     with eq show "?xs ! n = ?ys ! n"
       by simp
   qed
 next
   assume ?Q
   then have "nth_default dflt (strip_while (HOL.eq dflt) xs) = nth_default dflt (strip_while (HOL.eq dflt) ys)"
     by simp
   then show ?P
     by simp
 qed
 
 lemma nth_default_map2:
   \<open>nth_default d (map2 f xs ys) n = f (nth_default d1 xs n) (nth_default d2 ys n)\<close>
     if \<open>length xs = length ys\<close> and \<open>f d1 d2 = d\<close> for bs cs
 using that proof (induction xs ys arbitrary: n rule: list_induct2)
   case Nil
   then show ?case
     by simp
 next
   case (Cons x xs y ys)
   then show ?case
     by (cases n) simp_all
 qed
 
 end