Commit 95cee475 authored by Robbert Krebbers's avatar Robbert Krebbers

More big_opMS lemmas.

parent d5646054
...@@ -157,6 +157,14 @@ Proof. ...@@ -157,6 +157,14 @@ Proof.
rewrite multiplicity_difference, multiplicity_empty; omega. rewrite multiplicity_difference, multiplicity_empty; omega.
Qed. 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 *) (* Properties of the elements operation *)
Lemma gmultiset_elements_empty : elements ( : gmultiset A) = []. Lemma gmultiset_elements_empty : elements ( : gmultiset A) = [].
Proof. Proof.
......
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