Commit 3663aaf3 authored by Robbert Krebbers's avatar Robbert Krebbers

More big op lemmas.

parent 6d66d9d1
......@@ -267,6 +267,9 @@ Section gmap.
Lemma big_opM_lookup f m i x :
m !! i = Some x f i x [ map] ky m, f k y.
Proof. intros. rewrite big_opM_delete //. apply cmra_included_l. Qed.
Lemma big_opM_lookup_dom (f : K M) m i :
is_Some (m !! i) f i [ map] k_ m, f k.
Proof. intros [x ?]. by eapply (big_opM_lookup (λ i x, f i)). Qed.
Lemma big_opM_singleton f i x : ([ map] ky {[i:=x]}, f k y) f i x.
Proof.
......
......@@ -330,6 +330,9 @@ Section gmap.
Lemma big_sepM_lookup Φ m i x :
m !! i = Some x ([ map] ky m, Φ k y) Φ i x.
Proof. intros. apply uPred_included. by apply: big_opM_lookup. Qed.
Lemma big_sepM_lookup_dom (Φ : K uPred M) m i :
is_Some (m !! i) ([ map] k_ m, Φ k) Φ i.
Proof. intros [x ?]. by eapply (big_sepM_lookup (λ i x, Φ i)). Qed.
Lemma big_sepM_singleton Φ i x : ([ map] ky {[i:=x]}, Φ k y) Φ i x.
Proof. by rewrite big_opM_singleton. Qed.
......
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