diff --git a/theories/gmultiset.v b/theories/gmultiset.v index 51b1a9831c582f61474e9ab734bef50b86c31bce..0fab06bc05343dfdbd8759b4e2b3e607c75649b0 100644 --- a/theories/gmultiset.v +++ b/theories/gmultiset.v @@ -157,6 +157,14 @@ Proof. rewrite multiplicity_difference, multiplicity_empty; omega. Qed. +(* Order stuff *) +Lemma gmultiset_elem_of_subseteq x X : x ∈ X → {[ x ]} ⊆ X. +Proof. + rewrite elem_of_multiplicity. intros Hx y; destruct (decide (x = y)) as [->|]. + - rewrite multiplicity_singleton; omega. + - rewrite multiplicity_singleton_ne by done; omega. +Qed. + (* Properties of the elements operation *) Lemma gmultiset_elements_empty : elements (∅ : gmultiset A) = []. Proof.