# HG changeset patch # User nipkow # Date 1379400171 -7200 # Node ID c5096c22892b7cff3d83c9548608583cfafc021c # Parent 81e244e71986cf4d0f34204a984f38dd14e3cf16 added lemmas and made concerse executable diff -r 81e244e71986 -r c5096c22892b src/HOL/Relation.thy --- a/src/HOL/Relation.thy Tue Sep 17 01:11:37 2013 +0200 +++ b/src/HOL/Relation.thy Tue Sep 17 08:42:51 2013 +0200 @@ -680,6 +680,12 @@ "(r\\)\\ = r" by (fact converse_converse [to_pred]) +lemma converse_empty[simp]: "{}\ = {}" +by auto + +lemma converse_UNIV[simp]: "UNIV\ = UNIV" +by auto + lemma converse_relcomp: "(r O s)^-1 = s^-1 O r^-1" by blast @@ -762,7 +768,7 @@ lemma conversep_eq [simp]: "(op =)^--1 = op =" by (auto simp add: fun_eq_iff) -lemma converse_unfold: +lemma converse_unfold [code]: "r\ = {(y, x). (x, y) \ r}" by (simp add: set_eq_iff)