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 280a80df4..c7ccce543 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.
--
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