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Dan Frumin
iriscoq
Commits
0b7e25c2
Commit
0b7e25c2
authored
Feb 10, 2016
by
Ralf Jung
Browse files
make auth_closing less stupid
parent
05b7229d
Changes
2
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Inline
Sidebyside
algebra/auth.v
View file @
0b7e25c2
...
...
@@ 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 *.
...
...
program_logic/auth.v
View file @
0b7e25c2
...
...
@@ 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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