src/HOL/Relation.thy

 
 lemma refl_on_def' [nitpick_unfold, code]:
   "refl_on A r \<longleftrightarrow> (\<forall>(x, y) \<in> r. x \<in> A \<and> y \<in> A) \<and> (\<forall>x \<in> A. (x, x) \<in> r)"
   by (auto intro: refl_onI dest: refl_onD refl_onD1 refl_onD2)
 
-lemma reflp_equality [simp]: "reflp (=)"
-  by (simp add: reflp_def)
+lemma reflp_on_equality [simp]: "reflp_on A (=)"
+  by (simp add: reflp_on_def)
 
 lemma reflp_on_mono:
   "reflp_on A R \<Longrightarrow> (\<And>x y. x \<in> A \<Longrightarrow> y \<in> A \<Longrightarrow> R x y \<Longrightarrow> Q x y) \<Longrightarrow> reflp_on A Q"
   by (auto intro: reflp_onI dest: reflp_onD)