Commit 38d61951 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove "filter" accessor for big_sepS.

parent e5a3be94
......@@ -526,6 +526,17 @@ Section gset.
by rewrite !big_sepS_insert // IH pure_False // False_impl left_id.
Lemma big_sepS_filter_acc (P : A Prop) `{ y, Decision (P y)} Φ X Y :
( y, y Y P y y X)
([ set] y X, Φ y) -
([ set] y Y, P y Φ y)
(([ set] y Y, P y Φ y) - [ set] y X, Φ y).
intros ?. destruct (proj1 (subseteq_disjoint_union_L (filter P Y) X))
as (Z&->&?); first set_solver.
rewrite big_sepS_union // big_sepS_filter. by apply sep_mono_r, wand_intro_l.
Lemma big_sepS_sepS Φ Ψ X :
([ set] y X, Φ y Ψ y) ([ set] y X, Φ y) ([ set] y X, Ψ y).
Proof. apply: big_opS_opS. Qed.
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