author | nipkow |
Wed, 10 Nov 2021 08:36:50 +0100 | |
changeset 74744 | ed1e5ea25369 |
parent 74743 | 5ae76214565f |
child 74745 | f54c81fe84f2 |
src/HOL/List.thy | file | annotate | diff | comparison | revisions |
--- a/src/HOL/List.thy Tue Nov 09 19:47:24 2021 +0100 +++ b/src/HOL/List.thy Wed Nov 10 08:36:50 2021 +0100 @@ -1545,6 +1545,8 @@ lemma filter_empty_conv: "(filter P xs = []) = (\<forall>x\<in>set xs. \<not> P x)" by (induct xs) simp_all +lemmas empty_filter_conv = filter_empty_conv[THEN eq_iff_swap] + lemma filter_id_conv: "(filter P xs = xs) = (\<forall>x\<in>set xs. P x)" proof (induct xs) case (Cons x xs)