From 74639a53fd2fd6a38834a96499a7e6a1b47c1c18 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Mon, 10 Dec 2018 10:37:04 +0100 Subject: [PATCH] =?UTF-8?q?New=20lemma=20`Next=5Funinj=20x=20:=20=E2=88=83?= =?UTF-8?q?=20a,=20x=20=E2=89=A1=20Next=20a`.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This lemma allows one to get the witness out of a later, without having to use `later_car`, i.e. in a way that works in the on-paper version of the logic. --- theories/algebra/ofe.v | 2 ++ 1 file changed, 2 insertions(+) diff --git a/theories/algebra/ofe.v b/theories/algebra/ofe.v index fb39bc55a..716350954 100644 --- a/theories/algebra/ofe.v +++ b/theories/algebra/ofe.v @@ -1022,6 +1022,8 @@ Section later. Global Instance Later_inj n : Inj (dist n) (dist (S n)) (@Next A). Proof. by intros x y. Qed. + Lemma Next_uninj x : ∃ a, x ≡ Next a. + Proof. by exists (later_car x). Qed. Instance later_car_anti_contractive n : Proper (dist n ==> dist_later n) later_car. Proof. move=> [x] [y] /= Hxy. done. Qed. -- GitLab