From eb200cc0d13ca98823d11094de8c9f070565ffbb Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Tue, 10 Mar 2020 21:33:43 +0100 Subject: [PATCH] Add lemma `fupd_plain_laterN`. --- theories/bi/updates.v | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/theories/bi/updates.v b/theories/bi/updates.v index 7679b2924..1c3ecec3b 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. -- GitLab