added lemma reflclp_ident_if_reflp[simp]
authordesharna
Wed, 09 Nov 2022 15:37:21 +0100
changeset 76497 ebcfaddd3cb6
parent 76496 855b5f0456d8
child 76498 11077c158b37
added lemma reflclp_ident_if_reflp[simp]
NEWS
src/HOL/Transitive_Closure.thy
--- a/NEWS	Wed Nov 09 16:39:45 2022 +0100
+++ b/NEWS	Wed Nov 09 15:37:21 2022 +0100
@@ -51,6 +51,7 @@
   - Strengthened lemma reflp_rtranclp and renamed to reflp_on_rtranclp.
     Minor INCOMPATIBILITY.
   - Added lemmas.
+      reflclp_ident_if_reflp[simp]
       reflp_on_reflclp[simp]
 
 * Theory "HOL.Wellfounded":
--- a/src/HOL/Transitive_Closure.thy	Wed Nov 09 16:39:45 2022 +0100
+++ b/src/HOL/Transitive_Closure.thy	Wed Nov 09 15:37:21 2022 +0100
@@ -82,6 +82,9 @@
 lemma reflclp_idemp [simp]: "(P\<^sup>=\<^sup>=)\<^sup>=\<^sup>= = P\<^sup>=\<^sup>="
   by blast
 
+lemma reflclp_ident_if_reflp[simp]: "reflp R \<Longrightarrow> R\<^sup>=\<^sup>= = R"
+  by (auto dest: reflpD)
+
 
 subsection \<open>Reflexive-transitive closure\<close>