Some decidable agreement CMRA properties.

cbad1f38 · Robbert Krebbers · 96e5b762 · cbad1f38
Commit cbad1f38 authored Feb 26, 2016 by Robbert Krebbers
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algebra/dec_agree.v algebra/dec_agree.v +6 -3

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--- a/algebra/dec_agree.v
+++ b/algebra/dec_agree.v
@@ -49,10 +49,13 @@ Qed.
 Canonical Structure dec_agreeRA : cmraT := discreteRA dec_agree_ra.

 (* Some properties of this CMRA *)
-Lemma dec_agree_idemp (x : dec_agree A) : x ⋅ x ≡ x.
-Proof. destruct x; by repeat (simplify_eq/= || case_match). Qed.
+Lemma dec_agree_ne a b : a ≠ b → DecAgree a ⋅ DecAgree b = DecAgreeBot.
+Proof. intros. by rewrite /= decide_False. Qed.

-Lemma dec_agree_op_inv (x1 x2 : dec_agree A) : ✓ (x1 ⋅ x2) → x1 ≡ x2.
+Lemma dec_agree_idemp (x : dec_agree A) : x ⋅ x = x.
+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.
 End dec_agree.