Commit 6af9f587 authored by Ralf Jung's avatar Ralf Jung

prove auth_closing :)

parent 10ccbc24
......@@ -43,10 +43,9 @@ Section auth.
Context {Hφ : n, Proper (dist n ==> dist n) φ}.
Lemma auth_opened a γ :
(auth_inv γ auth_own γ a) ( a', φ (a a') own AuthI γ ( (a a') a)).
(auth_inv γ auth_own γ a) ( a', φ (a a') own AuthI γ ( (a a') a)).
Proof.
rewrite /auth_inv. rewrite [auth_own _ _]later_intro -later_sep.
apply later_mono. rewrite sep_exist_r. apply exist_elim=>b.
rewrite /auth_inv. rewrite sep_exist_r. apply exist_elim=>b.
rewrite /auth_own [(_ φ _)%I]commutative -associative -own_op.
rewrite own_valid_r auth_valid !sep_exist_l /=. apply exist_elim=>a'.
rewrite [ _]left_id -(exist_intro a').
......@@ -58,5 +57,25 @@ Section auth.
apply sep_mono; first done.
by rewrite sep_elim_l.
Qed.
(* TODO: This notion should probably be defined in algebra/,
with instances proven for the important constructions. *)
Definition auth_step a b :=
( n a' af, {S n} (a a') a a' {S n} af a
b a' {S n} b af {S n} (b a')).
Lemma auth_closing a a' b γ :
auth_step a b
(φ (b a') own AuthI γ ( (a a') a))
pvs N N (auth_inv γ auth_own γ b).
Proof.
intros Hstep. rewrite /auth_inv /auth_own -(exist_intro (b a')).
rewrite [(_ φ _)%I]commutative -associative.
rewrite -pvs_frame_l. apply sep_mono; first done.
rewrite -own_op. apply own_update.
apply auth_update=>n af Ha Heq. apply Hstep; first done.
by rewrite [af _]commutative.
Qed.
End auth.
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