Commit 15201439 authored by Ralf Jung's avatar Ralf Jung
Browse files

simplify the auth invariant

parent 21419737
......@@ -24,7 +24,7 @@ Arguments auth_own {_ _ _ _ _} _ _.
Definition auth_inv `{authG Λ Σ A}
(γ : gname) (φ : A iPropG Λ Σ) : iPropG Λ Σ :=
( a, ( a own γ ( a)) φ a)%I.
( a, own γ ( a) φ a)%I.
Definition auth_ctx`{authG Λ Σ A}
(γ : gname) (N : namespace) (φ : A iPropG Λ Σ) : iPropG Λ Σ :=
inv N (auth_inv γ φ).
......@@ -64,7 +64,7 @@ Section auth.
rewrite sep_exist_l. apply exist_elim=>γ. rewrite -(exist_intro γ).
trans ( auth_inv γ φ auth_own γ a)%I.
{ rewrite /auth_inv -(exist_intro a) later_sep.
rewrite -valid_intro // left_id. ecancel [▷ φ _]%I.
ecancel [ φ _]%I.
by rewrite -later_intro auth_own_eq -own_op auth_both_op. }
rewrite (inv_alloc N) /auth_ctx pvs_frame_r. apply pvs_mono.
by rewrite always_and_sep_l.
......@@ -78,8 +78,8 @@ Section auth.
(|={E}=> a', (a a') φ (a a') own γ ( (a a') a)).
rewrite /auth_inv. rewrite later_exist sep_exist_r. apply exist_elim=>b.
rewrite later_sep [((_ _))%I]pvs_timeless !pvs_frame_r. apply pvs_mono.
rewrite always_and_sep_l -!assoc discrete_valid. apply const_elim_sep_l=>Hv.
rewrite later_sep [( own _ _)%I]pvs_timeless !pvs_frame_r. apply pvs_mono.
rewrite own_valid_l discrete_valid -!assoc. apply const_elim_sep_l=>Hv.
rewrite auth_own_eq [(▷φ _ _)%I]comm assoc -own_op.
rewrite own_valid_r auth_validI /= and_elim_l sep_exist_l sep_exist_r /=.
apply exist_elim=>a'.
......@@ -87,7 +87,8 @@ Section auth.
apply (eq_rewrite b (a a') (λ x, x φ x own γ ( x a))%I).
{ by move=>n x y /timeless_iff ->. }
{ by eauto with I. }
rewrite -valid_intro // left_id comm. auto with I.
rewrite -valid_intro; last by apply Hv.
rewrite left_id comm. auto with I.
Lemma auth_closing `{!LocalUpdate Lv L} E γ a a' :
......@@ -99,7 +100,7 @@ Section auth.
(* TODO it would be really nice to use cancel here *)
rewrite later_sep [(_ ▷φ _)%I]comm -assoc.
rewrite -pvs_frame_l. apply sep_mono_r.
rewrite -valid_intro // left_id -later_intro -own_op.
rewrite -later_intro -own_op.
by apply own_update, (auth_local_update_l L).
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