1.1 --- a/src/HOL/Relation.thy Thu Jul 25 08:57:16 2013 +0200
1.2 +++ b/src/HOL/Relation.thy Thu Jul 25 12:25:07 2013 +0200
1.3 @@ -131,7 +131,6 @@
1.4 lemma SUP_Sup_eq2 [pred_set_conv]: "(\<Squnion>i\<in>S. (\<lambda>x y. (x, y) \<in> i)) = (\<lambda>x y. (x, y) \<in> \<Union>S)"
1.5 by (simp add: fun_eq_iff)
1.6
1.7 -
1.8 subsection {* Properties of relations *}
1.9
1.10 subsubsection {* Reflexivity *}
1.11 @@ -706,6 +705,12 @@
1.12 lemma converse_UNION: "(UNION S r)^-1 = (UN x:S. (r x)^-1)"
1.13 by blast
1.14
1.15 +lemma converse_mono: "r^-1 \<subseteq> s ^-1 \<longleftrightarrow> r \<subseteq> s"
1.16 + by auto
1.17 +
1.18 +lemma conversep_mono: "r^--1 \<le> s ^--1 \<longleftrightarrow> r \<le> s"
1.19 + by (fact converse_mono[to_pred])
1.20 +
1.21 lemma converse_Id [simp]: "Id^-1 = Id"
1.22 by blast
1.23