Commit 0b89b550 authored by Ralf Jung's avatar Ralf Jung
Browse files

Merge branch 'ralf/big_sepS' into 'master'

add big_sepS_insert_2' and big_sepS_union_2

See merge request iris/iris!787
parents 2f1129aa 608e43fe
Pipeline #65716 passed with stage
in 8 minutes and 35 seconds
......@@ -2548,6 +2548,24 @@ Section gset.
replace ({[x]} X) with X by set_solver.
auto.
Qed.
Lemma big_sepS_insert_2' {Φ X} x
`{!TCOr (Affine (Φ x)) (Absorbing (Φ x))} :
Φ x - ([ set] y X, Φ y) - ([ set] y X {[ x ]}, Φ y).
Proof. rewrite comm_L. by apply big_sepS_insert_2. Qed.
Lemma big_sepS_union_2 {Φ} X Y
`{! x, TCOr (Affine (Φ x)) (Absorbing (Φ x))} :
([ set] y X, Φ y) - ([ set] y Y, Φ y) - ([ set] y X Y, Φ y).
Proof.
apply wand_intro_r. induction X as [|x X ? IH] using set_ind_L.
{ by rewrite left_id_L big_sepS_empty left_id. }
rewrite big_sepS_insert // -assoc IH -assoc_L.
destruct (decide (x Y)).
{ replace ({[x]} (X Y)) with (X Y) by set_solver.
rewrite (big_sepS_delete _ _ x); last set_solver.
by rewrite assoc sep_elim_r. }
by rewrite big_sepS_insert; last set_solver.
Qed.
Lemma big_sepS_delete_2 {Φ X} x :
Affine (Φ x)
......
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