src/HOL/Library/Multiset.thy

--- a/src/HOL/Library/Multiset.thy	Tue Mar 04 15:19:08 2025 +0100
+++ b/src/HOL/Library/Multiset.thy	Tue Mar 04 16:07:55 2025 +0100
@@ -1337,6 +1337,9 @@
   qed
 qed
 
+lemma filter_mset_eq_mempty_iff: "filter_mset P A = {#} \<longleftrightarrow> (\<forall>x. x \<in># A \<longrightarrow> \<not>P x)"
+  by (auto simp: multiset_eq_iff count_eq_zero_iff)
+
 lemma filter_filter_mset: "filter_mset P (filter_mset Q M) = {#x \<in># M. Q x \<and> P x#}"
   by (auto simp: multiset_eq_iff)