Commit 6c3226cc authored by Dan Frumin's avatar Dan Frumin
Browse files

Add `big_sepM2_union_inv_r`.

parent 2a7833d4
......@@ -2005,6 +2005,20 @@ Section map2.
Proof. intros. rewrite big_sepM2_eq /big_sepM2_def. apply _. Qed.
End map2.
Lemma big_sepM2_union_inv_r `{Countable K} {A B}
(Φ : K A B PROP) (m1 m2 : gmap K B) (n : gmap K A) :
m1 ## m2
([ map] kx;y n;(m1 m2), Φ k x y)
n1 n2, n = n1 n2
([ map] kx;y n1;m1, Φ k x y)
([ map] kx;y n2;m2, Φ k x y).
Proof.
intros Hm. rewrite -(big_sepM2_flip Φ).
rewrite (big_sepM2_union_inv_l (λ k (x : B) y, Φ k y x)) //.
f_equiv=>n1. f_equiv=>n2. f_equiv.
by rewrite -!(big_sepM2_flip Φ).
Qed.
Lemma big_sepM_sepM2_diag `{Countable K} {A} (Φ : K A A PROP) (m : gmap K A) :
([ map] ky m, Φ k y y) -
([ map] ky1;y2 m;m, Φ k y1 y2).
......
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