proposition: Lemma gmultiset_subset_size X Y : X ⊂ Y → size X < size Y.
proof: Proof. intros HXY. assert (size (Y ∖ X) ≠ 0). { by apply gmultiset_size_non_empty_iff, gmultiset_non_empty_difference. } rewrite (gmultiset_disj_union_difference X Y), gmultiset_size_disj_union by auto using gmultiset_subset_subseteq. lia. Qed.
imports: stdpp(gmap) stdpp(options)