diff --git a/theories/gmultiset.v b/theories/gmultiset.v index 075af94c5844ab6d910c51e6a19b0a5edffe07ee..46486b49b33f973a708c89d08bb4b76b3b233418 100644 --- a/theories/gmultiset.v +++ b/theories/gmultiset.v @@ -570,6 +570,15 @@ Section more_lemmas. Lemma gmultiset_singleton_subseteq_l x X : {[+ x +]} ⊆ X ↔ x ∈ X. Proof. multiset_solver. Qed. + Lemma gmultiset_singleton_subseteq x y : + {[+ x +]} ⊆@{gmultiset A} {[+ y +]} ↔ x = y. + Proof. + split; [|multiset_solver]. + (* FIXME: [multiset_solver] should solve this *) + intros Hxy. specialize (Hxy x). + rewrite multiplicity_singleton, multiplicity_singleton' in Hxy. + case_decide; [done|lia]. + Qed. Lemma gmultiset_elem_of_subseteq X1 X2 x : x ∈ X1 → X1 ⊆ X2 → x ∈ X2. Proof. multiset_solver. Qed.