diff --git a/theories/bi/updates.v b/theories/bi/updates.v index 7679b2924fc9ea37e8f3d5374ed3bdac8a1d2df2..1c3ecec3b4e873a68ad801d84135d202ee1e6bf9 100644 --- a/theories/bi/updates.v +++ b/theories/bi/updates.v @@ -430,6 +430,12 @@ Section fupd_derived. Lemma fupd_plain_later E P `{!Plain P} : (▷ |={E}=> P) ⊢ |={E}=> ▷ ◇ P. Proof. by rewrite {1}(plain P) fupd_plainly_later. Qed. + Lemma fupd_plain_laterN E n P `{!Plain P} : (▷^n |={E}=> P) ⊢ |={E}=> ▷^n ◇ P. + Proof. + induction n as [|n IH]; simpl; [by rewrite -except_0_intro|]. + by rewrite IH fupd_plain_later except_0_laterN except_0_idemp. + Qed. + Lemma fupd_plain_forall_2 E {A} (Φ : A → PROP) `{!∀ x, Plain (Φ x)} : (∀ x, |={E}=> Φ x) ⊢ |={E}=> ∀ x, Φ x. Proof.