# HG changeset patch
# User desharna
# Date 1671658555 -3600
# Node ID 9d9a2731a4e33e41c7b39ac1a74459f9bd057297
# Parent  b4a9c907e062cc28d797fe4671912d1be90aa503
added lemmas irrefl_on_if_asym_on[simp] and irreflp_on_if_asymp_on[simp]

diff -r b4a9c907e062 -r 9d9a2731a4e3 NEWS
--- a/NEWS	Wed Dec 21 22:11:16 2022 +0100
+++ b/NEWS	Wed Dec 21 22:35:55 2022 +0100
@@ -75,11 +75,13 @@
       irrefl_onD
       irrefl_onI
       irrefl_on_converse[simp]
+      irrefl_on_if_asym_on[simp]
       irrefl_on_subset
       irreflpD
       irreflp_onD
       irreflp_onI
       irreflp_on_converse[simp]
+      irreflp_on_if_asymp_on[simp]
       irreflp_on_irrefl_on_eq[pred_set_conv]
       irreflp_on_subset
       linorder.totalp_on_ge[simp]
diff -r b4a9c907e062 -r 9d9a2731a4e3 src/HOL/Relation.thy
--- a/src/HOL/Relation.thy	Wed Dec 21 22:11:16 2022 +0100
+++ b/src/HOL/Relation.thy	Wed Dec 21 22:35:55 2022 +0100
@@ -393,6 +393,12 @@
 lemma asymp_on_subset: "asymp_on A R \<Longrightarrow> B \<subseteq> A \<Longrightarrow> asymp_on B R"
   by (auto simp: asymp_on_def)
 
+lemma irrefl_on_if_asym_on[simp]: "asym_on A r \<Longrightarrow> irrefl_on A r"
+  by (auto intro: irrefl_onI dest: asym_onD)
+
+lemma irreflp_on_if_asymp_on[simp]: "asymp_on A r \<Longrightarrow> irreflp_on A r"
+  by (rule irrefl_on_if_asym_on[to_pred])
+
 lemma (in preorder) asymp_on_less[simp]: "asymp_on A (<)"
   by (auto intro: dual_order.asym)