merged

--- a/NEWS	Tue Oct 11 18:30:09 2022 +0200
+++ b/NEWS	Tue Oct 11 18:52:01 2022 +0200
@@ -13,9 +13,15 @@
   - Strengthened lemma total_on_singleton. Minor INCOMPATIBILITY.
   - Added lemmas.
       antisym_if_asymp
+      antisymp_ge[simp]
+      antisymp_greater[simp]
       antisymp_if_asymp
+      antisymp_le[simp]
+      antisymp_less[simp]
       irreflD
       irreflpD
+      reflp_ge[simp]
+      reflp_le[simp]
       totalp_on_singleton[simp]
 
 

--- a/src/HOL/Relation.thy	Tue Oct 11 18:30:09 2022 +0200
+++ b/src/HOL/Relation.thy	Tue Oct 11 18:52:01 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>
 
@@ -435,6 +441,18 @@
 lemma antisymp_if_asymp: "asymp R \<Longrightarrow> antisymp R"
   by (rule antisym_if_asym[to_pred])
 
+lemma (in preorder) antisymp_less[simp]: "antisymp (<)"
+  by (rule antisymp_if_asymp[OF asymp_less])
+
+lemma (in preorder) antisymp_greater[simp]: "antisymp (>)"
+  by (rule antisymp_if_asymp[OF asymp_greater])
+
+lemma (in order) antisymp_le[simp]: "antisymp (\<le>)"
+  by (simp add: antisympI)
+
+lemma (in order) antisymp_ge[simp]: "antisymp (\<ge>)"
+  by (simp add: antisympI)
+
 
 subsubsection \<open>Transitivity\<close>