# HG changeset patch
# User haftmann
# Date 1614112908 0
# Node ID beaff25452d28a2ba1fd375492f33b43c253241e
# Parent  2ac92ba88d6bb1ded2db0a87f0b25bf2893b099e
more specific name

diff -r 2ac92ba88d6b -r beaff25452d2 NEWS
--- a/NEWS	Tue Feb 23 20:41:48 2021 +0000
+++ b/NEWS	Tue Feb 23 20:41:48 2021 +0000
@@ -18,6 +18,9 @@
 more small lemmas. Some theorems that were stated awkwardly before were
 corrected. Minor INCOMPATIBILITY.
 
+* Theory "Permutation" in HOL-Library has been renamed to the more
+specific "List_Permutation".
+
 
 *** ML ***
 
diff -r 2ac92ba88d6b -r beaff25452d2 src/HOL/Algebra/Divisibility.thy
--- a/src/HOL/Algebra/Divisibility.thy	Tue Feb 23 20:41:48 2021 +0000
+++ b/src/HOL/Algebra/Divisibility.thy	Tue Feb 23 20:41:48 2021 +0000
@@ -6,7 +6,7 @@
 section \<open>Divisibility in monoids and rings\<close>
 
 theory Divisibility
-  imports "HOL-Library.Permutation" Coset Group
+  imports "HOL-Library.List_Permutation" Coset Group
 begin
 
 section \<open>Factorial Monoids\<close>
diff -r 2ac92ba88d6b -r beaff25452d2 src/HOL/Library/Library.thy
--- a/src/HOL/Library/Library.thy	Tue Feb 23 20:41:48 2021 +0000
+++ b/src/HOL/Library/Library.thy	Tue Feb 23 20:41:48 2021 +0000
@@ -50,6 +50,7 @@
   Lattice_Constructions
   Linear_Temporal_Logic_on_Streams
   ListVector
+  List_Permutation
   Lub_Glb
   Mapping
   Monad_Syntax
@@ -66,7 +67,6 @@
   Pattern_Aliases
   Periodic_Fun
   Perm
-  Permutation
   Permutations
   Poly_Mapping
   Power_By_Squaring
diff -r 2ac92ba88d6b -r beaff25452d2 src/HOL/Library/List_Permutation.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/List_Permutation.thy	Tue Feb 23 20:41:48 2021 +0000
@@ -0,0 +1,230 @@
+(*  Title:      HOL/Library/List_Permutation.thy
+    Author:     Lawrence C Paulson and Thomas M Rasmussen and Norbert Voelker
+*)
+
+section \<open>Permuted Lists\<close>
+
+theory List_Permutation
+imports Multiset
+begin
+
+inductive perm :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"  (infixr \<open><~~>\<close> 50)
+where
+  Nil [intro!]: "[] <~~> []"
+| swap [intro!]: "y # x # l <~~> x # y # l"
+| Cons [intro!]: "xs <~~> ys \<Longrightarrow> z # xs <~~> z # ys"
+| trans [intro]: "xs <~~> ys \<Longrightarrow> ys <~~> zs \<Longrightarrow> xs <~~> zs"
+
+proposition perm_refl [iff]: "l <~~> l"
+  by (induct l) auto
+
+
+subsection \<open>Some examples of rule induction on permutations\<close>
+
+proposition perm_empty_imp: "[] <~~> ys \<Longrightarrow> ys = []"
+  by (induction "[] :: 'a list" ys pred: perm) simp_all
+
+
+text \<open>\medskip This more general theorem is easier to understand!\<close>
+
+proposition perm_length: "xs <~~> ys \<Longrightarrow> length xs = length ys"
+  by (induct pred: perm) simp_all
+
+proposition perm_sym: "xs <~~> ys \<Longrightarrow> ys <~~> xs"
+  by (induct pred: perm) auto
+
+
+subsection \<open>Ways of making new permutations\<close>
+
+text \<open>We can insert the head anywhere in the list.\<close>
+
+proposition perm_append_Cons: "a # xs @ ys <~~> xs @ a # ys"
+  by (induct xs) auto
+
+proposition perm_append_swap: "xs @ ys <~~> ys @ xs"
+  by (induct xs) (auto intro: perm_append_Cons)
+
+proposition perm_append_single: "a # xs <~~> xs @ [a]"
+  by (rule perm.trans [OF _ perm_append_swap]) simp
+
+proposition perm_rev: "rev xs <~~> xs"
+  by (induct xs) (auto intro!: perm_append_single intro: perm_sym)
+
+proposition perm_append1: "xs <~~> ys \<Longrightarrow> l @ xs <~~> l @ ys"
+  by (induct l) auto
+
+proposition perm_append2: "xs <~~> ys \<Longrightarrow> xs @ l <~~> ys @ l"
+  by (blast intro!: perm_append_swap perm_append1)
+
+
+subsection \<open>Further results\<close>
+
+proposition perm_empty [iff]: "[] <~~> xs \<longleftrightarrow> xs = []"
+  by (blast intro: perm_empty_imp)
+
+proposition perm_empty2 [iff]: "xs <~~> [] \<longleftrightarrow> xs = []"
+  using perm_sym by auto
+
+proposition perm_sing_imp: "ys <~~> xs \<Longrightarrow> xs = [y] \<Longrightarrow> ys = [y]"
+  by (induct pred: perm) auto
+
+proposition perm_sing_eq [iff]: "ys <~~> [y] \<longleftrightarrow> ys = [y]"
+  by (blast intro: perm_sing_imp)
+
+proposition perm_sing_eq2 [iff]: "[y] <~~> ys \<longleftrightarrow> ys = [y]"
+  by (blast dest: perm_sym)
+
+
+subsection \<open>Removing elements\<close>
+
+proposition perm_remove: "x \<in> set ys \<Longrightarrow> ys <~~> x # remove1 x ys"
+  by (induct ys) auto
+
+
+text \<open>\medskip Congruence rule\<close>
+
+proposition perm_remove_perm: "xs <~~> ys \<Longrightarrow> remove1 z xs <~~> remove1 z ys"
+  by (induct pred: perm) auto
+
+proposition remove_hd [simp]: "remove1 z (z # xs) = xs"
+  by auto
+
+proposition cons_perm_imp_perm: "z # xs <~~> z # ys \<Longrightarrow> xs <~~> ys"
+  by (drule perm_remove_perm [where z = z]) auto
+
+proposition cons_perm_eq [iff]: "z#xs <~~> z#ys \<longleftrightarrow> xs <~~> ys"
+  by (meson cons_perm_imp_perm perm.Cons)
+
+proposition append_perm_imp_perm: "zs @ xs <~~> zs @ ys \<Longrightarrow> xs <~~> ys"
+  by (induct zs arbitrary: xs ys rule: rev_induct) auto
+
+proposition perm_append1_eq [iff]: "zs @ xs <~~> zs @ ys \<longleftrightarrow> xs <~~> ys"
+  by (blast intro: append_perm_imp_perm perm_append1)
+
+proposition perm_append2_eq [iff]: "xs @ zs <~~> ys @ zs \<longleftrightarrow> xs <~~> ys"
+  by (meson perm.trans perm_append1_eq perm_append_swap)
+
+theorem mset_eq_perm: "mset xs = mset ys \<longleftrightarrow> xs <~~> ys"
+proof
+  assume "mset xs = mset ys"
+  then show "xs <~~> ys"
+  proof (induction xs arbitrary: ys)
+    case (Cons x xs)
+    then have "x \<in> set ys"
+      using mset_eq_setD by fastforce
+    then show ?case
+      by (metis Cons.IH Cons.prems mset_remove1 perm.Cons perm.trans perm_remove perm_sym remove_hd)
+  qed auto
+next
+  assume "xs <~~> ys"
+  then show "mset xs = mset ys"
+    by induction (simp_all add: union_ac)
+qed
+
+proposition mset_le_perm_append: "mset xs \<subseteq># mset ys \<longleftrightarrow> (\<exists>zs. xs @ zs <~~> ys)"
+  apply (rule iffI)
+  apply (metis mset_append mset_eq_perm mset_subset_eq_exists_conv surjD surj_mset)
+  by (metis mset_append mset_eq_perm mset_subset_eq_exists_conv)
+
+proposition perm_set_eq: "xs <~~> ys \<Longrightarrow> set xs = set ys"
+  by (metis mset_eq_perm mset_eq_setD)
+
+proposition perm_distinct_iff: "xs <~~> ys \<Longrightarrow> distinct xs = distinct ys"
+  by (metis card_distinct distinct_card perm_length perm_set_eq)
+
+theorem eq_set_perm_remdups: "set xs = set ys \<Longrightarrow> remdups xs <~~> remdups ys"
+proof (induction xs arbitrary: ys rule: length_induct)
+  case (1 xs)
+  show ?case
+  proof (cases "remdups xs")
+    case Nil
+    with "1.prems" show ?thesis
+      using "1.prems" by auto
+  next
+    case (Cons x us)
+    then have "x \<in> set (remdups ys)"
+      using "1.prems" set_remdups by fastforce
+    then show ?thesis
+      using "1.prems" mset_eq_perm set_eq_iff_mset_remdups_eq by blast
+  qed
+qed 
+
+proposition perm_remdups_iff_eq_set: "remdups x <~~> remdups y \<longleftrightarrow> set x = set y"
+  by (metis List.set_remdups perm_set_eq eq_set_perm_remdups)
+
+theorem permutation_Ex_bij:
+  assumes "xs <~~> ys"
+  shows "\<exists>f. bij_betw f {..<length xs} {..<length ys} \<and> (\<forall>i<length xs. xs ! i = ys ! (f i))"
+  using assms
+proof induct
+  case Nil
+  then show ?case
+    unfolding bij_betw_def by simp
+next
+  case (swap y x l)
+  show ?case
+  proof (intro exI[of _ "Fun.swap 0 1 id"] conjI allI impI)
+    show "bij_betw (Fun.swap 0 1 id) {..<length (y # x # l)} {..<length (x # y # l)}"
+      by (auto simp: bij_betw_def)
+    fix i
+    assume "i < length (y # x # l)"
+    show "(y # x # l) ! i = (x # y # l) ! (Fun.swap 0 1 id) i"
+      by (cases i) (auto simp: Fun.swap_def gr0_conv_Suc)
+  qed
+next
+  case (Cons xs ys z)
+  then obtain f where bij: "bij_betw f {..<length xs} {..<length ys}"
+    and perm: "\<forall>i<length xs. xs ! i = ys ! (f i)"
+    by blast
+  let ?f = "\<lambda>i. case i of Suc n \<Rightarrow> Suc (f n) | 0 \<Rightarrow> 0"
+  show ?case
+  proof (intro exI[of _ ?f] allI conjI impI)
+    have *: "{..<length (z#xs)} = {0} \<union> Suc ` {..<length xs}"
+            "{..<length (z#ys)} = {0} \<union> Suc ` {..<length ys}"
+      by (simp_all add: lessThan_Suc_eq_insert_0)
+    show "bij_betw ?f {..<length (z#xs)} {..<length (z#ys)}"
+      unfolding *
+    proof (rule bij_betw_combine)
+      show "bij_betw ?f (Suc ` {..<length xs}) (Suc ` {..<length ys})"
+        using bij unfolding bij_betw_def
+        by (auto intro!: inj_onI imageI dest: inj_onD simp: image_comp comp_def)
+    qed (auto simp: bij_betw_def)
+    fix i
+    assume "i < length (z # xs)"
+    then show "(z # xs) ! i = (z # ys) ! (?f i)"
+      using perm by (cases i) auto
+  qed
+next
+  case (trans xs ys zs)
+  then obtain f g
+    where bij: "bij_betw f {..<length xs} {..<length ys}" "bij_betw g {..<length ys} {..<length zs}"
+    and perm: "\<forall>i<length xs. xs ! i = ys ! (f i)" "\<forall>i<length ys. ys ! i = zs ! (g i)"
+    by blast
+  show ?case
+  proof (intro exI[of _ "g \<circ> f"] conjI allI impI)
+    show "bij_betw (g \<circ> f) {..<length xs} {..<length zs}"
+      using bij by (rule bij_betw_trans)
+    fix i
+    assume "i < length xs"
+    with bij have "f i < length ys"
+      unfolding bij_betw_def by force
+    with \<open>i < length xs\<close> show "xs ! i = zs ! (g \<circ> f) i"
+      using trans(1,3)[THEN perm_length] perm by auto
+  qed
+qed
+
+proposition perm_finite: "finite {B. B <~~> A}"
+proof (rule finite_subset[where B="{xs. set xs \<subseteq> set A \<and> length xs \<le> length A}"])
+ show "finite {xs. set xs \<subseteq> set A \<and> length xs \<le> length A}"
+   using finite_lists_length_le by blast
+next
+ show "{B. B <~~> A} \<subseteq> {xs. set xs \<subseteq> set A \<and> length xs \<le> length A}"
+   by (clarsimp simp add: perm_length perm_set_eq)
+qed
+
+proposition perm_swap:
+    assumes "i < length xs" "j < length xs"
+    shows "xs[i := xs ! j, j := xs ! i] <~~> xs"
+  using assms by (simp add: mset_eq_perm[symmetric] mset_swap)
+
+end
diff -r 2ac92ba88d6b -r beaff25452d2 src/HOL/Library/Permutation.thy
--- a/src/HOL/Library/Permutation.thy	Tue Feb 23 20:41:48 2021 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,230 +0,0 @@
-(*  Title:      HOL/Library/Permutation.thy
-    Author:     Lawrence C Paulson and Thomas M Rasmussen and Norbert Voelker
-*)
-
-section \<open>Permutations\<close>
-
-theory Permutation
-imports Multiset
-begin
-
-inductive perm :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"  (infixr \<open><~~>\<close> 50)
-where
-  Nil [intro!]: "[] <~~> []"
-| swap [intro!]: "y # x # l <~~> x # y # l"
-| Cons [intro!]: "xs <~~> ys \<Longrightarrow> z # xs <~~> z # ys"
-| trans [intro]: "xs <~~> ys \<Longrightarrow> ys <~~> zs \<Longrightarrow> xs <~~> zs"
-
-proposition perm_refl [iff]: "l <~~> l"
-  by (induct l) auto
-
-
-subsection \<open>Some examples of rule induction on permutations\<close>
-
-proposition perm_empty_imp: "[] <~~> ys \<Longrightarrow> ys = []"
-  by (induction "[] :: 'a list" ys pred: perm) simp_all
-
-
-text \<open>\medskip This more general theorem is easier to understand!\<close>
-
-proposition perm_length: "xs <~~> ys \<Longrightarrow> length xs = length ys"
-  by (induct pred: perm) simp_all
-
-proposition perm_sym: "xs <~~> ys \<Longrightarrow> ys <~~> xs"
-  by (induct pred: perm) auto
-
-
-subsection \<open>Ways of making new permutations\<close>
-
-text \<open>We can insert the head anywhere in the list.\<close>
-
-proposition perm_append_Cons: "a # xs @ ys <~~> xs @ a # ys"
-  by (induct xs) auto
-
-proposition perm_append_swap: "xs @ ys <~~> ys @ xs"
-  by (induct xs) (auto intro: perm_append_Cons)
-
-proposition perm_append_single: "a # xs <~~> xs @ [a]"
-  by (rule perm.trans [OF _ perm_append_swap]) simp
-
-proposition perm_rev: "rev xs <~~> xs"
-  by (induct xs) (auto intro!: perm_append_single intro: perm_sym)
-
-proposition perm_append1: "xs <~~> ys \<Longrightarrow> l @ xs <~~> l @ ys"
-  by (induct l) auto
-
-proposition perm_append2: "xs <~~> ys \<Longrightarrow> xs @ l <~~> ys @ l"
-  by (blast intro!: perm_append_swap perm_append1)
-
-
-subsection \<open>Further results\<close>
-
-proposition perm_empty [iff]: "[] <~~> xs \<longleftrightarrow> xs = []"
-  by (blast intro: perm_empty_imp)
-
-proposition perm_empty2 [iff]: "xs <~~> [] \<longleftrightarrow> xs = []"
-  using perm_sym by auto
-
-proposition perm_sing_imp: "ys <~~> xs \<Longrightarrow> xs = [y] \<Longrightarrow> ys = [y]"
-  by (induct pred: perm) auto
-
-proposition perm_sing_eq [iff]: "ys <~~> [y] \<longleftrightarrow> ys = [y]"
-  by (blast intro: perm_sing_imp)
-
-proposition perm_sing_eq2 [iff]: "[y] <~~> ys \<longleftrightarrow> ys = [y]"
-  by (blast dest: perm_sym)
-
-
-subsection \<open>Removing elements\<close>
-
-proposition perm_remove: "x \<in> set ys \<Longrightarrow> ys <~~> x # remove1 x ys"
-  by (induct ys) auto
-
-
-text \<open>\medskip Congruence rule\<close>
-
-proposition perm_remove_perm: "xs <~~> ys \<Longrightarrow> remove1 z xs <~~> remove1 z ys"
-  by (induct pred: perm) auto
-
-proposition remove_hd [simp]: "remove1 z (z # xs) = xs"
-  by auto
-
-proposition cons_perm_imp_perm: "z # xs <~~> z # ys \<Longrightarrow> xs <~~> ys"
-  by (drule perm_remove_perm [where z = z]) auto
-
-proposition cons_perm_eq [iff]: "z#xs <~~> z#ys \<longleftrightarrow> xs <~~> ys"
-  by (meson cons_perm_imp_perm perm.Cons)
-
-proposition append_perm_imp_perm: "zs @ xs <~~> zs @ ys \<Longrightarrow> xs <~~> ys"
-  by (induct zs arbitrary: xs ys rule: rev_induct) auto
-
-proposition perm_append1_eq [iff]: "zs @ xs <~~> zs @ ys \<longleftrightarrow> xs <~~> ys"
-  by (blast intro: append_perm_imp_perm perm_append1)
-
-proposition perm_append2_eq [iff]: "xs @ zs <~~> ys @ zs \<longleftrightarrow> xs <~~> ys"
-  by (meson perm.trans perm_append1_eq perm_append_swap)
-
-theorem mset_eq_perm: "mset xs = mset ys \<longleftrightarrow> xs <~~> ys"
-proof
-  assume "mset xs = mset ys"
-  then show "xs <~~> ys"
-  proof (induction xs arbitrary: ys)
-    case (Cons x xs)
-    then have "x \<in> set ys"
-      using mset_eq_setD by fastforce
-    then show ?case
-      by (metis Cons.IH Cons.prems mset_remove1 perm.Cons perm.trans perm_remove perm_sym remove_hd)
-  qed auto
-next
-  assume "xs <~~> ys"
-  then show "mset xs = mset ys"
-    by induction (simp_all add: union_ac)
-qed
-
-proposition mset_le_perm_append: "mset xs \<subseteq># mset ys \<longleftrightarrow> (\<exists>zs. xs @ zs <~~> ys)"
-  apply (rule iffI)
-  apply (metis mset_append mset_eq_perm mset_subset_eq_exists_conv surjD surj_mset)
-  by (metis mset_append mset_eq_perm mset_subset_eq_exists_conv)
-
-proposition perm_set_eq: "xs <~~> ys \<Longrightarrow> set xs = set ys"
-  by (metis mset_eq_perm mset_eq_setD)
-
-proposition perm_distinct_iff: "xs <~~> ys \<Longrightarrow> distinct xs = distinct ys"
-  by (metis card_distinct distinct_card perm_length perm_set_eq)
-
-theorem eq_set_perm_remdups: "set xs = set ys \<Longrightarrow> remdups xs <~~> remdups ys"
-proof (induction xs arbitrary: ys rule: length_induct)
-  case (1 xs)
-  show ?case
-  proof (cases "remdups xs")
-    case Nil
-    with "1.prems" show ?thesis
-      using "1.prems" by auto
-  next
-    case (Cons x us)
-    then have "x \<in> set (remdups ys)"
-      using "1.prems" set_remdups by fastforce
-    then show ?thesis
-      using "1.prems" mset_eq_perm set_eq_iff_mset_remdups_eq by blast
-  qed
-qed 
-
-proposition perm_remdups_iff_eq_set: "remdups x <~~> remdups y \<longleftrightarrow> set x = set y"
-  by (metis List.set_remdups perm_set_eq eq_set_perm_remdups)
-
-theorem permutation_Ex_bij:
-  assumes "xs <~~> ys"
-  shows "\<exists>f. bij_betw f {..<length xs} {..<length ys} \<and> (\<forall>i<length xs. xs ! i = ys ! (f i))"
-  using assms
-proof induct
-  case Nil
-  then show ?case
-    unfolding bij_betw_def by simp
-next
-  case (swap y x l)
-  show ?case
-  proof (intro exI[of _ "Fun.swap 0 1 id"] conjI allI impI)
-    show "bij_betw (Fun.swap 0 1 id) {..<length (y # x # l)} {..<length (x # y # l)}"
-      by (auto simp: bij_betw_def)
-    fix i
-    assume "i < length (y # x # l)"
-    show "(y # x # l) ! i = (x # y # l) ! (Fun.swap 0 1 id) i"
-      by (cases i) (auto simp: Fun.swap_def gr0_conv_Suc)
-  qed
-next
-  case (Cons xs ys z)
-  then obtain f where bij: "bij_betw f {..<length xs} {..<length ys}"
-    and perm: "\<forall>i<length xs. xs ! i = ys ! (f i)"
-    by blast
-  let ?f = "\<lambda>i. case i of Suc n \<Rightarrow> Suc (f n) | 0 \<Rightarrow> 0"
-  show ?case
-  proof (intro exI[of _ ?f] allI conjI impI)
-    have *: "{..<length (z#xs)} = {0} \<union> Suc ` {..<length xs}"
-            "{..<length (z#ys)} = {0} \<union> Suc ` {..<length ys}"
-      by (simp_all add: lessThan_Suc_eq_insert_0)
-    show "bij_betw ?f {..<length (z#xs)} {..<length (z#ys)}"
-      unfolding *
-    proof (rule bij_betw_combine)
-      show "bij_betw ?f (Suc ` {..<length xs}) (Suc ` {..<length ys})"
-        using bij unfolding bij_betw_def
-        by (auto intro!: inj_onI imageI dest: inj_onD simp: image_comp comp_def)
-    qed (auto simp: bij_betw_def)
-    fix i
-    assume "i < length (z # xs)"
-    then show "(z # xs) ! i = (z # ys) ! (?f i)"
-      using perm by (cases i) auto
-  qed
-next
-  case (trans xs ys zs)
-  then obtain f g
-    where bij: "bij_betw f {..<length xs} {..<length ys}" "bij_betw g {..<length ys} {..<length zs}"
-    and perm: "\<forall>i<length xs. xs ! i = ys ! (f i)" "\<forall>i<length ys. ys ! i = zs ! (g i)"
-    by blast
-  show ?case
-  proof (intro exI[of _ "g \<circ> f"] conjI allI impI)
-    show "bij_betw (g \<circ> f) {..<length xs} {..<length zs}"
-      using bij by (rule bij_betw_trans)
-    fix i
-    assume "i < length xs"
-    with bij have "f i < length ys"
-      unfolding bij_betw_def by force
-    with \<open>i < length xs\<close> show "xs ! i = zs ! (g \<circ> f) i"
-      using trans(1,3)[THEN perm_length] perm by auto
-  qed
-qed
-
-proposition perm_finite: "finite {B. B <~~> A}"
-proof (rule finite_subset[where B="{xs. set xs \<subseteq> set A \<and> length xs \<le> length A}"])
- show "finite {xs. set xs \<subseteq> set A \<and> length xs \<le> length A}"
-   using finite_lists_length_le by blast
-next
- show "{B. B <~~> A} \<subseteq> {xs. set xs \<subseteq> set A \<and> length xs \<le> length A}"
-   by (clarsimp simp add: perm_length perm_set_eq)
-qed
-
-proposition perm_swap:
-    assumes "i < length xs" "j < length xs"
-    shows "xs[i := xs ! j, j := xs ! i] <~~> xs"
-  using assms by (simp add: mset_eq_perm[symmetric] mset_swap)
-
-end
diff -r 2ac92ba88d6b -r beaff25452d2 src/HOL/Probability/ex/Koepf_Duermuth_Countermeasure.thy
--- a/src/HOL/Probability/ex/Koepf_Duermuth_Countermeasure.thy	Tue Feb 23 20:41:48 2021 +0000
+++ b/src/HOL/Probability/ex/Koepf_Duermuth_Countermeasure.thy	Tue Feb 23 20:41:48 2021 +0000
@@ -3,7 +3,7 @@
 section \<open>Formalization of a Countermeasure by Koepf \& Duermuth 2009\<close>
 
 theory Koepf_Duermuth_Countermeasure
-  imports "HOL-Probability.Information" "HOL-Library.Permutation"
+  imports "HOL-Probability.Information" "HOL-Library.List_Permutation"
 begin
 
 lemma SIGMA_image_vimage: