Commit d920fcd4 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Generalize `big_sepL_sepL2` to become bidirectional, add same kind of lemma for maps.

parent 0e5917cf
......@@ -653,15 +653,12 @@ Section sep_list2.
by rewrite IH.
Qed.
Lemma big_sepL_sepL2 (Φ : nat A PROP) (Ψ : nat B PROP)
(l1 : list A) (l2 : list B) :
Lemma big_sepL_sepL2 (Φ1 : nat A PROP) (Φ2 : nat B PROP) l1 l2 :
length l1 = length l2
([ list] ky1 l1, Φ k y1) -
([ list] ky2 l2, Ψ k y2) -
([ list] ky1;y2 l1;l2, Φ k y1 Ψ k y2).
([ list] ky1;y2 l1;l2, Φ1 k y1 Φ2 k y2)
([ list] ky1 l1, Φ1 k y1) ([ list] ky2 l2, Φ2 k y2).
Proof.
intros Hlen. apply wand_intro_r.
rewrite big_sepL_sep_zip // big_sepL2_alt pure_True // left_id //.
intros. rewrite -big_sepL_sep_zip // big_sepL2_alt pure_True // left_id //.
Qed.
Global Instance big_sepL2_nil_persistent Φ :
......@@ -1173,6 +1170,12 @@ Lemma big_sepM_sep_zip `{Countable K} {A B}
Proof. apply big_opM_sep_zip. Qed.
(** ** Big ops over two maps *)
Lemma big_sepM2_alt `{Countable K} {A B} (Φ : K A B PROP) m1 m2 :
([ map] ky1;y2 m1; m2, Φ k y1 y2)
k, is_Some (m1 !! k) is_Some (m2 !! k)
[ map] k xy map_zip m1 m2, Φ k xy.1 xy.2.
Proof. by rewrite big_sepM2_eq. Qed.
Section map2.
Context `{Countable K} {A B : Type}.
Implicit Types Φ Ψ : K A B PROP.
......@@ -1537,6 +1540,14 @@ Section map2.
apply big_sepM2_mono. eauto.
Qed.
Lemma big_sepM_sepM2 (Φ1 : K A PROP) (Φ2 : K B PROP) m1 m2 :
( k, is_Some (m1 !! k) is_Some (m2 !! k))
([ map] ky1;y2 m1;m2, Φ1 k y1 Φ2 k y2)
([ map] ky1 m1, Φ1 k y1) ([ map] ky2 m2, Φ2 k y2).
Proof.
intros. rewrite -big_sepM_sep_zip // big_sepM2_alt pure_True // left_id //.
Qed.
Global Instance big_sepM2_empty_persistent Φ :
Persistent ([ map] ky1;y2 ; , Φ k y1 y2).
Proof. rewrite big_sepM2_empty. apply _. Qed.
......
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