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Commit 50d5afed authored by Ralf Jung's avatar Ralf Jung
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add big_sepS_insert_2

parent 4b47dc0b
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......@@ -2071,6 +2071,14 @@ Section gset.
Lemma big_sepS_insert Φ X x :
x X ([ set] y {[ x ]} X, Φ y) ⊣⊢ (Φ x [ set] y X, Φ y).
Proof. apply big_opS_insert. Qed.
Lemma big_sepS_insert_2 `{!BiAffine PROP} Φ X x :
(Φ x [ set] y X, Φ y) ([ set] y {[ x ]} X, Φ y).
Proof.
destruct (decide (x X)).
- rewrite bi.sep_elim_r. replace ({[x]} X) with X by set_solver.
done.
- rewrite -big_sepS_insert //.
Qed.
Lemma big_sepS_fn_insert {B} (Ψ : A B PROP) f X x b :
x X
......
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