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e4b58ebf
Commit
e4b58ebf
authored
Feb 11, 2016
by
Ralf Jung
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change auth_pvs to have a more genrally useful form
parent
ee3b01dd
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program_logic/auth.v
program_logic/auth.v
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program_logic/auth.v
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e4b58ebf
...
...
@@ -77,13 +77,12 @@ Section auth.
(* Notice how the user has to prove that `b⋅a'` is valid at all
step-indices. However, since A is timeless, that should not be
a restriction. *)
(* TODO The form of the lemma, with a very specific post-condition, is not ideal. *)
Lemma
auth_pvs
`
{!
LocalUpdate
Lv
L
}
E
P
(
Q
:
A
→
iProp
Λ
(
globalC
Σ
))
γ
a
:
Lemma
auth_pvs
`
{!
LocalUpdate
Lv
L
}
E
P
Q
γ
a
:
nclose
N
⊆
E
→
(
auth_ctx
γ
★
auth_own
γ
a
★
(
∀
a'
,
▷φ
(
a
⋅
a'
)
-
★
pvs
(
E
∖
nclose
N
)
(
E
∖
nclose
N
)
(
■
(
Lv
a
∧
✓
(
L
a
⋅
a'
))
★
▷φ
(
L
a
⋅
a'
)
★
Q
(
L
a
))))
⊑
pvs
E
E
(
auth_own
γ
(
L
a
)
★
Q
(
L
a
))
.
(
■
(
Lv
a
∧
✓
(
L
a
⋅
a'
))
★
▷φ
(
L
a
⋅
a'
)
★
(
auth_own
γ
(
L
a
)
-
★
Q
))))
⊑
pvs
E
E
Q
.
Proof
.
rewrite
/
auth_ctx
=>
HN
.
rewrite
-[
pvs
E
E
_
]
pvs_open_close
;
last
eassumption
.
...
...
@@ -91,11 +90,11 @@ Section auth.
rewrite
associative
auth_opened
!
pvs_frame_r
!
sep_exist_r
.
apply
pvs_strip_pvs
.
apply
exist_elim
=>
a'
.
rewrite
(
forall_elim
a'
).
rewrite
[(
▷
_
★
_
)%
I
]
commutative
.
rewrite
-[((
_
★
▷
_
)
★
_
)%
I
]
associative
wand_elim_r
pvs_frame_l
.
apply
pvs_strip_pvs
.
rewrite
commutative
-!
associative
.
apply
const_elim_sep_l
=>-[
HL
Hv
]
.
rewrite
associative
[(
_
★
Q
_
)%
I
]
commutative
-
associative
auth_closing
//
;
[
].
erewrite
pvs_frame_l
.
apply
pvs_mono
.
rewrite
a
ssociative
[(
_
★
Q
_
)%
I
]
commutative
associative
.
apply
sep_mono
;
last
done
.
by
rewrite
commutative
.
rewrite
-[((
_
★
▷
_
)
★
_
)%
I
]
associative
wand_elim_r
pvs_frame_l
.
apply
pvs_strip_pvs
.
rewrite
commutative
-!
associative
.
apply
const_elim_sep_l
=>-[
HL
Hv
].
rewrite
associative
[(
_
★
(
_
-
★
_
))%
I
]
commutative
-
associative
.
rewrite
a
uth_closing
//
;
[].
erewrite
pvs_frame_l
.
apply
pvs_mono
.
by
rewrite
associative
[(
_
★
▷
_
)%
I
]
commutative
-
associative
wand_elim_l
.
Qed
.
End
auth
.
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