diff --git a/iris/bi/big_op.v b/iris/bi/big_op.v index 60a087b43df6629ed76ebbe53adc9514ee1dae57..71d2496bccf1ccc77b7feee8470feefded09d2a9 100644 --- a/iris/bi/big_op.v +++ b/iris/bi/big_op.v @@ -2090,6 +2090,14 @@ Section gset. Lemma big_sepS_delete Φ X x : x ∈ X → ([∗ set] y ∈ X, Φ y) ⊣⊢ Φ x ∗ [∗ set] y ∈ X ∖ {[ x ]}, Φ y. Proof. apply big_opS_delete. Qed. + Lemma big_sepS_delete_2 `{!BiAffine PROP} Φ X x : + Φ x ∗ ([∗ set] y ∈ X ∖ {[ x ]}, Φ y) ⊢ [∗ set] y ∈ X, Φ y. + Proof. + destruct (decide (x ∈ X)). + - rewrite -big_sepS_delete //. + - replace (X ∖ {[x]}) with X by set_solver. + rewrite bi.sep_elim_r. done. + Qed. Lemma big_sepS_elem_of Φ X x `{!Absorbing (Φ x)} : x ∈ X → ([∗ set] y ∈ X, Φ y) ⊢ Φ x.