src/HOL/Library/List_Lexorder.thy
 changeset 72166 bb37571139bf parent 71766 1249b998e377 child 72169 2d7619fc0e1a
```--- a/src/HOL/Library/List_Lexorder.thy	Mon Aug 17 15:42:59 2020 +0100
+++ b/src/HOL/Library/List_Lexorder.thy	Tue Aug 18 14:44:59 2020 +0100
@@ -26,17 +26,20 @@
let ?r = "{(u, v::'a). u < v}"
have tr: "trans ?r"
using trans_def by fastforce
+  have *: "antisym {(u, v::'a). u < v}"
+    using antisym_def by fastforce
have \<section>: False
if "(xs,ys) \<in> lexord ?r" "(ys,xs) \<in> lexord ?r" for xs ys :: "'a list"
proof -
have "(xs,xs) \<in> lexord ?r"
-      using that transD [OF lexord_transI [OF tr]] by blast
+      using lexord_trans that tr * by blast
then show False
by (meson case_prodD lexord_irreflexive less_irrefl mem_Collect_eq)
qed
show "xs \<le> xs" for xs :: "'a list" by (simp add: list_le_def)
show "xs \<le> zs" if "xs \<le> ys" and "ys \<le> zs" for xs ys zs :: "'a list"
-    using that transD [OF lexord_transI [OF tr]] by (auto simp add: list_le_def list_less_def)
+    using that transD [OF lexord_transI [OF tr]] *
+    by (auto simp add: list_le_def list_less_def)
show "xs = ys" if "xs \<le> ys" "ys \<le> xs" for xs ys :: "'a list"
using \<section> that list_le_def list_less_def by blast
show "xs < ys \<longleftrightarrow> xs \<le> ys \<and> \<not> ys \<le> xs" for xs ys :: "'a list"
@@ -70,7 +73,7 @@
lemma Nil_less_Cons [simp]: "[] < a # x"