proposition: Lemma gmultiset_elem_of_dom x X : x ∈ dom X ↔ x ∈ X.
proof: Proof. unfold dom, gmultiset_dom, elem_of at 2, gmultiset_elem_of, multiplicity. destruct X as [X]; simpl; rewrite elem_of_dom, <-not_eq_None_Some. destruct (X !! x); naive_solver lia. Qed.
imports: stdpp(gmap) stdpp(options)