Commit 0b7e25c2 authored by Ralf Jung's avatar Ralf Jung

make auth_closing less stupid

parent 05b7229d
......@@ -147,8 +147,12 @@ Proof. done. Qed.
Lemma auth_both_op a b : Auth (Excl a) b a b.
Proof. by rewrite /op /auth_op /= left_id. Qed.
(* FIXME tentative name. Or maybe remove this notion entirely. *)
Definition auth_step a a' b b' :=
n af, {n} a a {n} a' af b {n} b' af {n} b.
Lemma auth_update a a' b b' :
( n af, {n} a a {n} a' af b {n} b' af {n} b)
auth_step a a' b b'
a a' ~~> b b'.
Proof.
move=> Hab [[?| |] bf1] n // =>-[[bf2 Ha] ?]; do 2 red; simpl in *.
......
......@@ -58,14 +58,8 @@ Section auth.
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, {n} (a a') a a' {n} af a
b a' {n} b af {n} (b a')).
Lemma auth_closing a a' b γ :
auth_step a b
auth_step (a a') a (b a') b
(φ (b a') own AuthI γ ( (a a') a))
pvs N N (auth_inv γ auth_own γ b).
Proof.
......@@ -73,8 +67,7 @@ Section auth.
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.
by apply auth_update.
Qed.
End auth.
......
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