# HG changeset patch
# User nipkow
# Date 1527595559 -7200
# Node ID e9b5f25f6712aaa9016cc85e43d2fbbbd6e98932
# Parent  c551d8acaa4206bc3d3ddee9935d53cca285bd03
canonical names

diff -r c551d8acaa42 -r e9b5f25f6712 src/HOL/Library/Fun_Lexorder.thy
--- a/src/HOL/Library/Fun_Lexorder.thy	Mon May 28 23:15:30 2018 +0100
+++ b/src/HOL/Library/Fun_Lexorder.thy	Tue May 29 14:05:59 2018 +0200
@@ -1,6 +1,6 @@
 (* Author: Florian Haftmann, TU Muenchen *)
 
-section \<open>Lexical order on functions\<close>
+section \<open>Lexicographic order on functions\<close>
 
 theory Fun_Lexorder
 imports Main
diff -r c551d8acaa42 -r e9b5f25f6712 src/HOL/Library/List_Lexorder.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/List_Lexorder.thy	Tue May 29 14:05:59 2018 +0200
@@ -0,0 +1,121 @@
+(*  Title:      HOL/Library/List_Lexorder.thy
+    Author:     Norbert Voelker
+*)
+
+section \<open>Lexicographic order on lists\<close>
+
+theory List_Lexorder
+imports Main
+begin
+
+instantiation list :: (ord) ord
+begin
+
+definition
+  list_less_def: "xs < ys \<longleftrightarrow> (xs, ys) \<in> lexord {(u, v). u < v}"
+
+definition
+  list_le_def: "(xs :: _ list) \<le> ys \<longleftrightarrow> xs < ys \<or> xs = ys"
+
+instance ..
+
+end
+
+instance list :: (order) order
+proof
+  fix xs :: "'a list"
+  show "xs \<le> xs" by (simp add: list_le_def)
+next
+  fix xs ys zs :: "'a list"
+  assume "xs \<le> ys" and "ys \<le> zs"
+  then show "xs \<le> zs"
+    apply (auto simp add: list_le_def list_less_def)
+    apply (rule lexord_trans)
+    apply (auto intro: transI)
+    done
+next
+  fix xs ys :: "'a list"
+  assume "xs \<le> ys" and "ys \<le> xs"
+  then show "xs = ys"
+    apply (auto simp add: list_le_def list_less_def)
+    apply (rule lexord_irreflexive [THEN notE])
+    defer
+    apply (rule lexord_trans)
+    apply (auto intro: transI)
+    done
+next
+  fix xs ys :: "'a list"
+  show "xs < ys \<longleftrightarrow> xs \<le> ys \<and> \<not> ys \<le> xs"
+    apply (auto simp add: list_less_def list_le_def)
+    defer
+    apply (rule lexord_irreflexive [THEN notE])
+    apply auto
+    apply (rule lexord_irreflexive [THEN notE])
+    defer
+    apply (rule lexord_trans)
+    apply (auto intro: transI)
+    done
+qed
+
+instance list :: (linorder) linorder
+proof
+  fix xs ys :: "'a list"
+  have "(xs, ys) \<in> lexord {(u, v). u < v} \<or> xs = ys \<or> (ys, xs) \<in> lexord {(u, v). u < v}"
+    by (rule lexord_linear) auto
+  then show "xs \<le> ys \<or> ys \<le> xs"
+    by (auto simp add: list_le_def list_less_def)
+qed
+
+instantiation list :: (linorder) distrib_lattice
+begin
+
+definition "(inf :: 'a list \<Rightarrow> _) = min"
+
+definition "(sup :: 'a list \<Rightarrow> _) = max"
+
+instance
+  by standard (auto simp add: inf_list_def sup_list_def max_min_distrib2)
+
+end
+
+lemma not_less_Nil [simp]: "\<not> x < []"
+  by (simp add: list_less_def)
+
+lemma Nil_less_Cons [simp]: "[] < a # x"
+  by (simp add: list_less_def)
+
+lemma Cons_less_Cons [simp]: "a # x < b # y \<longleftrightarrow> a < b \<or> a = b \<and> x < y"
+  by (simp add: list_less_def)
+
+lemma le_Nil [simp]: "x \<le> [] \<longleftrightarrow> x = []"
+  unfolding list_le_def by (cases x) auto
+
+lemma Nil_le_Cons [simp]: "[] \<le> x"
+  unfolding list_le_def by (cases x) auto
+
+lemma Cons_le_Cons [simp]: "a # x \<le> b # y \<longleftrightarrow> a < b \<or> a = b \<and> x \<le> y"
+  unfolding list_le_def by auto
+
+instantiation list :: (order) order_bot
+begin
+
+definition "bot = []"
+
+instance
+  by standard (simp add: bot_list_def)
+
+end
+
+lemma less_list_code [code]:
+  "xs < ([]::'a::{equal, order} list) \<longleftrightarrow> False"
+  "[] < (x::'a::{equal, order}) # xs \<longleftrightarrow> True"
+  "(x::'a::{equal, order}) # xs < y # ys \<longleftrightarrow> x < y \<or> x = y \<and> xs < ys"
+  by simp_all
+
+lemma less_eq_list_code [code]:
+  "x # xs \<le> ([]::'a::{equal, order} list) \<longleftrightarrow> False"
+  "[] \<le> (xs::'a::{equal, order} list) \<longleftrightarrow> True"
+  "(x::'a::{equal, order}) # xs \<le> y # ys \<longleftrightarrow> x < y \<or> x = y \<and> xs \<le> ys"
+  by simp_all
+
+end
diff -r c551d8acaa42 -r e9b5f25f6712 src/HOL/Library/List_lexord.thy
--- a/src/HOL/Library/List_lexord.thy	Mon May 28 23:15:30 2018 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,121 +0,0 @@
-(*  Title:      HOL/Library/List_lexord.thy
-    Author:     Norbert Voelker
-*)
-
-section \<open>Lexicographic order on lists\<close>
-
-theory List_lexord
-imports Main
-begin
-
-instantiation list :: (ord) ord
-begin
-
-definition
-  list_less_def: "xs < ys \<longleftrightarrow> (xs, ys) \<in> lexord {(u, v). u < v}"
-
-definition
-  list_le_def: "(xs :: _ list) \<le> ys \<longleftrightarrow> xs < ys \<or> xs = ys"
-
-instance ..
-
-end
-
-instance list :: (order) order
-proof
-  fix xs :: "'a list"
-  show "xs \<le> xs" by (simp add: list_le_def)
-next
-  fix xs ys zs :: "'a list"
-  assume "xs \<le> ys" and "ys \<le> zs"
-  then show "xs \<le> zs"
-    apply (auto simp add: list_le_def list_less_def)
-    apply (rule lexord_trans)
-    apply (auto intro: transI)
-    done
-next
-  fix xs ys :: "'a list"
-  assume "xs \<le> ys" and "ys \<le> xs"
-  then show "xs = ys"
-    apply (auto simp add: list_le_def list_less_def)
-    apply (rule lexord_irreflexive [THEN notE])
-    defer
-    apply (rule lexord_trans)
-    apply (auto intro: transI)
-    done
-next
-  fix xs ys :: "'a list"
-  show "xs < ys \<longleftrightarrow> xs \<le> ys \<and> \<not> ys \<le> xs"
-    apply (auto simp add: list_less_def list_le_def)
-    defer
-    apply (rule lexord_irreflexive [THEN notE])
-    apply auto
-    apply (rule lexord_irreflexive [THEN notE])
-    defer
-    apply (rule lexord_trans)
-    apply (auto intro: transI)
-    done
-qed
-
-instance list :: (linorder) linorder
-proof
-  fix xs ys :: "'a list"
-  have "(xs, ys) \<in> lexord {(u, v). u < v} \<or> xs = ys \<or> (ys, xs) \<in> lexord {(u, v). u < v}"
-    by (rule lexord_linear) auto
-  then show "xs \<le> ys \<or> ys \<le> xs"
-    by (auto simp add: list_le_def list_less_def)
-qed
-
-instantiation list :: (linorder) distrib_lattice
-begin
-
-definition "(inf :: 'a list \<Rightarrow> _) = min"
-
-definition "(sup :: 'a list \<Rightarrow> _) = max"
-
-instance
-  by standard (auto simp add: inf_list_def sup_list_def max_min_distrib2)
-
-end
-
-lemma not_less_Nil [simp]: "\<not> x < []"
-  by (simp add: list_less_def)
-
-lemma Nil_less_Cons [simp]: "[] < a # x"
-  by (simp add: list_less_def)
-
-lemma Cons_less_Cons [simp]: "a # x < b # y \<longleftrightarrow> a < b \<or> a = b \<and> x < y"
-  by (simp add: list_less_def)
-
-lemma le_Nil [simp]: "x \<le> [] \<longleftrightarrow> x = []"
-  unfolding list_le_def by (cases x) auto
-
-lemma Nil_le_Cons [simp]: "[] \<le> x"
-  unfolding list_le_def by (cases x) auto
-
-lemma Cons_le_Cons [simp]: "a # x \<le> b # y \<longleftrightarrow> a < b \<or> a = b \<and> x \<le> y"
-  unfolding list_le_def by auto
-
-instantiation list :: (order) order_bot
-begin
-
-definition "bot = []"
-
-instance
-  by standard (simp add: bot_list_def)
-
-end
-
-lemma less_list_code [code]:
-  "xs < ([]::'a::{equal, order} list) \<longleftrightarrow> False"
-  "[] < (x::'a::{equal, order}) # xs \<longleftrightarrow> True"
-  "(x::'a::{equal, order}) # xs < y # ys \<longleftrightarrow> x < y \<or> x = y \<and> xs < ys"
-  by simp_all
-
-lemma less_eq_list_code [code]:
-  "x # xs \<le> ([]::'a::{equal, order} list) \<longleftrightarrow> False"
-  "[] \<le> (xs::'a::{equal, order} list) \<longleftrightarrow> True"
-  "(x::'a::{equal, order}) # xs \<le> y # ys \<longleftrightarrow> x < y \<or> x = y \<and> xs \<le> ys"
-  by simp_all
-
-end
diff -r c551d8acaa42 -r e9b5f25f6712 src/HOL/ROOT
--- a/src/HOL/ROOT	Mon May 28 23:15:30 2018 +0100
+++ b/src/HOL/ROOT	Tue May 29 14:05:59 2018 +0200
@@ -29,7 +29,7 @@
     Library
     (*conflicting type class instantiations and dependent applications*)
     Finite_Lattice
-    List_lexord
+    List_Lexorder
     Prefix_Order
     Product_Lexorder
     Product_Order
diff -r c551d8acaa42 -r e9b5f25f6712 src/HOL/ex/Radix_Sort.thy
--- a/src/HOL/ex/Radix_Sort.thy	Mon May 28 23:15:30 2018 +0100
+++ b/src/HOL/ex/Radix_Sort.thy	Tue May 29 14:05:59 2018 +0200
@@ -2,7 +2,7 @@
 
 theory Radix_Sort
 imports
-  "HOL-Library.List_lexord" 
+  "HOL-Library.List_Lexorder" 
   "HOL-Library.Sublist" 
   "HOL-Library.Multiset" 
 begin