Commit b48f3087 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove big_sepM_delete.

parent 0fa2fdcf
...@@ -139,6 +139,9 @@ Section gmap. ...@@ -139,6 +139,9 @@ Section gmap.
Lemma big_sepM_insert Φ (m : gmap K A) i x : 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). 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. 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). Lemma big_sepM_singleton Φ i x : Π★{map {[i := x]}} Φ ⊣⊢ (Φ i x).
Proof. Proof.
rewrite -insert_empty big_sepM_insert/=; last auto using lookup_empty. rewrite -insert_empty big_sepM_insert/=; last auto using lookup_empty.
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