Commit f72340bc authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

More derived auth properties.

parent 0024ac1f
......@@ -111,6 +111,8 @@ Proof.
destruct x as [[[?|]|] ?]; simpl; try done.
setoid_rewrite <-cmra_discrete_included_iff; naive_solver eauto using 0.
Lemma auth_valid_discrete_2 `{CMRADiscrete A} a b : ( a b) b a a.
Proof. by rewrite auth_valid_discrete /= left_id. Qed.
Lemma authoritative_valid x : x authoritative x.
Proof. by destruct x as [[[]|]]. Qed.
......@@ -189,6 +191,10 @@ Lemma auth_frag_op a b : ◯ (a ⋅ b) ≡ ◯ a ⋅ ◯ b.
Proof. done. Qed.
Lemma auth_both_op a b : Auth (Excl' a) b a b.
Proof. by rewrite /op /auth_op /= left_id. Qed.
Lemma auth_frag_mono a b : a b a b.
Proof. intros [c ->]. rewrite auth_frag_op. apply cmra_included_l. Qed.
Lemma auth_auth_valid a : a ( a).
Proof. intros; split; simpl; auto using ucmra_unit_leastN. Qed.
Lemma auth_update a af b :
a ~l~> b @ Some af (a af) a ~~> (b af) b.
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