# HG changeset patch # User desharna # Date 1671106705 -3600 # Node ID 878ed0fcb5105309ff72f8cf6234732683397749 # Parent e9f3f2b0c0a70f28ebfd80ff8d29d513c1d5418e added lemmas antisym_on_subset and antisymp_on_subset diff -r e9f3f2b0c0a7 -r 878ed0fcb510 NEWS --- a/NEWS Thu Dec 15 12:32:01 2022 +0100 +++ b/NEWS Thu Dec 15 13:18:25 2022 +0100 @@ -45,10 +45,12 @@ antisym_if_asymp antisym_onD antisym_onI + antisym_on_subset antisymp_if_asymp antisymp_onD antisymp_onI antisymp_on_antisym_on_eq[pred_set_conv] + antisymp_on_subset asym_if_irrefl_and_trans asymp_if_irreflp_and_transp irreflD diff -r e9f3f2b0c0a7 -r 878ed0fcb510 src/HOL/Relation.thy --- a/src/HOL/Relation.thy Thu Dec 15 12:32:01 2022 +0100 +++ b/src/HOL/Relation.thy Thu Dec 15 13:18:25 2022 +0100 @@ -447,7 +447,13 @@ "antisymp_on A (\x y. (x, y) \ r) \ antisym_on A r" by (simp add: antisym_on_def antisymp_on_def) -lemmas antisymp_antisym_eq = antisymp_on_antisym_on_eq[of UNIV] +lemmas antisymp_antisym_eq = antisymp_on_antisym_on_eq[of UNIV] \ \For backward compatibility\ + +lemma antisym_on_subset: "antisym_on A r \ B \ A \ antisym_on B r" + by (auto simp: antisym_on_def) + +lemma antisymp_on_subset: "antisymp_on A R \ B \ A \ antisymp_on B R" + by (auto simp: antisymp_on_def) lemma antisym_onI: "(\x y. x \ A \ y \ A \ (x, y) \ r \ (y, x) \ r \ x = y) \ antisym_on A r"