Commit 6af9f587 by 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.
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!