From 143fbc524ec6c9f0215a9b0a9e8f8b1730837360 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers Date: Thu, 6 Oct 2016 10:09:24 +0200 Subject: [PATCH] Prove that the dec_agree CMRA is total. --- algebra/dec_agree.v | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/algebra/dec_agree.v b/algebra/dec_agree.v index 280a80df..c7ccce54 100644 --- a/algebra/dec_agree.v +++ b/algebra/dec_agree.v @@ -31,21 +31,19 @@ Instance dec_agree_pcore : PCore (dec_agree A) := Some. Definition dec_agree_ra_mixin : RAMixin (dec_agree A). Proof. - split. - - apply _. - - intros x y cx ? [=<-]; eauto. - - apply _. + apply ra_total_mixin; apply _ || eauto. - intros [?|] [?|] [?|]; by repeat (simplify_eq/= || case_match). - intros [?|] [?|]; by repeat (simplify_eq/= || case_match). - - intros [?|] ? [=<-]; by repeat (simplify_eq/= || case_match). - intros [?|]; by repeat (simplify_eq/= || case_match). - - intros [?|] [?|] ?? [=<-]; eauto. - by intros [?|] [?|] ?. Qed. Canonical Structure dec_agreeR : cmraT := discreteR (dec_agree A) dec_agree_ra_mixin. +Global Instance dec_agree_total : CMRATotal dec_agreeR. +Proof. intros x. by exists x. Qed. + (* Some properties of this CMRA *) Global Instance dec_agree_persistent (x : dec_agreeR) : Persistent x. Proof. by constructor. Qed. @@ -59,8 +57,10 @@ Proof. destruct x; by rewrite /= ?decide_True. Qed. Lemma dec_agree_op_inv (x1 x2 : dec_agree A) : ✓ (x1 ⋅ x2) → x1 = x2. Proof. destruct x1, x2; by repeat (simplify_eq/= || case_match). Qed. -Lemma DecAgree_included a b : DecAgree a ≼ DecAgree b → a = b. -Proof. intros [[c|] [=]%leibniz_equiv_iff]. by simplify_option_eq. Qed. +Lemma DecAgree_included a b : DecAgree a ≼ DecAgree b ↔ a = b. +Proof. + split. intros [[c|] [=]%leibniz_equiv]. by simplify_option_eq. by intros ->. +Qed. End dec_agree. Arguments dec_agreeC : clear implicits. -- GitLab