src/HOL/Set.thy
changeset 70614 6a2c982363e9
parent 69986 f2d327275065
child 71827 5e315defb038
--- a/src/HOL/Set.thy	Sun Aug 25 22:17:24 2019 +0200
+++ b/src/HOL/Set.thy	Tue Aug 27 17:08:51 2019 +0200
@@ -1863,6 +1863,9 @@
 definition pairwise :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> 'a set \<Rightarrow> bool"
   where "pairwise R S \<longleftrightarrow> (\<forall>x \<in> S. \<forall>y \<in> S. x \<noteq> y \<longrightarrow> R x y)"
 
+lemma pairwise_alt: "pairwise R S \<longleftrightarrow> (\<forall>x\<in>S. \<forall>y\<in>S-{x}. R x y)"
+by (auto simp add: pairwise_def)
+
 lemma pairwise_trivial [simp]: "pairwise (\<lambda>i j. j \<noteq> i) I"
   by (auto simp: pairwise_def)