From b48f30878ae3789c2ba6c59c6e67120ae93b848f Mon Sep 17 00:00:00 2001
From: Robbert Krebbers <mail@robbertkrebbers.nl>
Date: Tue, 24 May 2016 15:45:09 +0200
Subject: [PATCH] Prove big_sepM_delete.

---
 algebra/upred_big_op.v | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/algebra/upred_big_op.v b/algebra/upred_big_op.v
index 65023fa60..6702eb075 100644
--- a/algebra/upred_big_op.v
+++ b/algebra/upred_big_op.v
@@ -139,6 +139,9 @@ Section gmap.
   Lemma big_sepM_insert Φ (m : gmap K A) i x :
     m !! i = None → Π★{map <[i:=x]> m} Φ ⊣⊢ (Φ i x ★ Π★{map m} Φ).
   Proof. intros ?; by rewrite /uPred_big_sepM map_to_list_insert. Qed.
+  Lemma big_sepM_delete Φ (m : gmap K A) i x :
+    m !! i = Some x → Π★{map m} Φ ⊣⊢ (Φ i x ★ Π★{map delete i m} Φ).
+  Proof. intros. by rewrite -big_sepM_insert ?lookup_delete // insert_delete. Qed.
   Lemma big_sepM_singleton Φ i x : Π★{map {[i := x]}} Φ ⊣⊢ (Φ i x).
   Proof.
     rewrite -insert_empty big_sepM_insert/=; last auto using lookup_empty.
-- 
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