More big_opMS lemmas.

95cee475 · Robbert Krebbers · d5646054 · 95cee475
Commit 95cee475 authored Nov 18, 2016 by Robbert Krebbers
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theories/gmultiset.v theories/gmultiset.v +8 -0

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--- 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.