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Commit dad8a9a7 authored by Robbert Krebbers's avatar Robbert Krebbers
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Misc property about the product CMRA.

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...@@ -580,6 +580,10 @@ Section prod. ...@@ -580,6 +580,10 @@ Section prod.
Persistent x → Persistent y → Persistent (x,y). Persistent x → Persistent y → Persistent (x,y).
Proof. by split. Qed. Proof. by split. Qed.
Lemma pair_split `{CMRAUnit A, CMRAUnit B} (x : A) (y : B) :
(x, y) ≡ (x, ∅) ⋅ (∅, y).
Proof. constructor; by rewrite /= ?left_id ?right_id. Qed.
Lemma prod_update x y : x.1 ~~> y.1 → x.2 ~~> y.2 → x ~~> y. Lemma prod_update x y : x.1 ~~> y.1 → x.2 ~~> y.2 → x ~~> y.
Proof. intros ?? n z [??]; split; simpl in *; auto. Qed. Proof. intros ?? n z [??]; split; simpl in *; auto. Qed.
Lemma prod_updateP P1 P2 (Q : A * B → Prop) x : Lemma prod_updateP P1 P2 (Q : A * B → Prop) x :
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