Commit 6cb0f4d2 authored by Robbert Krebbers's avatar Robbert Krebbers

Some lemmas about discreteness.

parent fc9e25a5
Pipeline #5629 passed with stages
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......@@ -555,11 +555,15 @@ Proof.
split; first by rewrite cmra_valid_validN.
eauto using cmra_discrete_valid, cmra_validN_le with lia.
Qed.
Lemma cmra_discrete_valid_iff_0 `{CmraDiscrete A} n x : {0} x {n} x.
Proof. by rewrite -!cmra_discrete_valid_iff. Qed.
Lemma cmra_discrete_included_iff `{OfeDiscrete A} n x y : x y x {n} y.
Proof.
split; first by apply cmra_included_includedN.
intros [z ->%(discrete_iff _ _)]; eauto using cmra_included_l.
Qed.
Lemma cmra_discrete_included_iff_0 `{OfeDiscrete A} n x y : x {0} y x {n} y.
Proof. by rewrite -!cmra_discrete_included_iff. Qed.
(** Cancelable elements *)
Global Instance cancelable_proper : Proper (equiv ==> iff) (@Cancelable A).
......
......@@ -190,9 +190,7 @@ Section ofe.
split; intros; auto. apply (discrete _), dist_le with n; auto with lia.
Qed.
Lemma discrete_iff_0 n (x : A) `{!Discrete x} y : x {0} y x {n} y.
Proof.
split=> ?. by apply equiv_dist, (discrete _). eauto using dist_le with lia.
Qed.
Proof. by rewrite -!discrete_iff. Qed.
End ofe.
(** Contractive functions *)
......
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