--- a/NEWS Mon Oct 10 19:07:54 2022 +0200
+++ b/NEWS Tue Oct 11 11:07:07 2022 +0200
@@ -16,6 +16,8 @@
antisymp_if_asymp
irreflD
irreflpD
+ reflp_ge[simp]
+ reflp_le[simp]
totalp_on_singleton[simp]
--- a/src/HOL/Relation.thy Mon Oct 10 19:07:54 2022 +0200
+++ b/src/HOL/Relation.thy Tue Oct 11 11:07:07 2022 +0200
@@ -256,6 +256,12 @@
lemma reflp_mono: "reflp R \<Longrightarrow> (\<And>x y. R x y \<Longrightarrow> Q x y) \<Longrightarrow> reflp Q"
by (rule reflp_on_mono[of UNIV R Q]) simp_all
+lemma (in preorder) reflp_le[simp]: "reflp (\<le>)"
+ by (simp add: reflpI)
+
+lemma (in preorder) reflp_ge[simp]: "reflp (\<ge>)"
+ by (simp add: reflpI)
+
subsubsection \<open>Irreflexivity\<close>