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PierreMarie Pédrot
Iris
Commits
53f179de
Commit
53f179de
authored
Jul 09, 2018
by
Ralf Jung
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shrink proof of timestamp_sub
parent
67abfa93
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theories/heap_lang/lib/atomic_snapshot.v
theories/heap_lang/lib/atomic_snapshot.v
+7
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theories/heap_lang/lib/atomic_snapshot.v
View file @
53f179de
...
...
@@ 217,29 +217,19 @@ Section atomic_snapshot.
iMod
(
own_op
with
"Ht"
)
as
"[Ht● Ht◯]"
.
iModIntro
.
iFrame
.
Qed
.
Lemma
fmap_undo
{
A
B
}
(
f
:
A
>
B
)
(
m
:
gmap
Z
A
)
k
v
:
f
<$>
m
!!
k
=
Some
v
>
exists
v'
,
m
!!
k
=
Some
v'
/\
v
=
f
v'
.
Proof
.
intros
Hl
.
destruct
(
m
!!
k
)
;
inversion
Hl
.
subst
.
eauto
.
Qed
.
Lemma
timestamp_sub
γ
(
T1
T2
:
gmap
Z
val
)
:
own
γ
(
●
gmap_to_UR
T1
)
∗
own
γ
(
◯
gmap_to_UR
T2
)

∗
⌜
forall
t
x
,
T2
!!
t
=
Some
x
>
T1
!!
t
=
Some
x
⌝
.
Proof
.
iIntros
"[Hγ⚫ Hγ◯]"
.
iDestruct
(
own_valid_2
with
"Hγ⚫ Hγ◯"
)
as
%[
H
Hv
]%
auth_valid_discrete_2
.
iPureIntro
.
intros
t
x
Ht
.
pose
proof
(
iffLR
(
lookup_included
(
gmap_to_UR
T2
)
(
gmap_to_UR
T1
))
H
t
)
as
Hsub
.
repeat
rewrite
lookup_fmap
in
Hsub
.
rewrite
Ht
in
Hsub
.
simpl
in
Hsub
.
pose
proof
(
mk_is_Some
(
Some
(
to_agree
x
))
_
eq_refl
)
as
Hsome
.
pose
proof
(
is_Some_included
_
_
Hsub
Hsome
)
as
Hsome'
;
clear
Hsome
.
destruct
Hsome'
as
[
c
Heqx
].
rewrite
Heqx
in
Hsub
.
apply
(
iffLR
(
Some_included_total
_
_
))
in
Hsub
.
destruct
(
fmap_undo
to_agree
_
_
_
Heqx
)
as
[
c'
[
Heq1
Heq2
]].
subst
.
apply
to_agree_included
in
Hsub
.
apply
leibniz_equiv
in
Hsub
.
subst
.
done
.
%[
H
Hv
]%
auth_valid_discrete_2
.
iPureIntro
.
intros
t
x
HT2
.
pose
proof
(
iffLR
(
lookup_included
(
gmap_to_UR
T2
)
(
gmap_to_UR
T1
))
H
t
)
as
Ht
.
rewrite
!
lookup_fmap
HT2
/=
in
Ht
.
destruct
(
is_Some_included
_
_
Ht
)
as
[?
[
t2
[
Ht2
>]]%
fmap_Some_1
]
;
first
by
eauto
.
revert
Ht
.
rewrite
Ht2
Some_included_total
to_agree_included
.
fold_leibniz
.
by
intros
>.
Qed
.
Lemma
writeY_spec
e
(
y2
:
val
)
γ
p
:
...
...
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