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Tej Chajed
iris
Commits
692b8570
Commit
692b8570
authored
Nov 28, 2016
by
Ralf Jung
Browse files
Add a local update for auth (needed for nested auth)
Proof was done by Hai & me
parent
1bc26dc9
Changes
1
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Inline
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algebra/auth.v
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692b8570
...
...
@@ 219,6 +219,33 @@ Lemma auth_update_alloc a a' b' : (a,∅) ~l~> (a',b') → ● a ~~> ● a' ⋅
Proof
.
intros
.
rewrite
(
right_id
_
_
(
●
a
)).
by
apply
auth_update
.
Qed
.
Lemma
auth_update_dealloc
a
b
a'
:
(
a
,
b
)
~l
~>
(
a'
,
∅
)
→
●
a
⋅
◯
b
~~>
●
a'
.
Proof
.
intros
.
rewrite
(
right_id
_
_
(
●
a'
)).
by
apply
auth_update
.
Qed
.
Lemma
auth_local_update
(
a
b0
b1
a'
b0'
b1'
:
A
)
:
(
b0
,
b1
)
~l
~>
(
b0'
,
b1'
)
→
b0'
≼
a'
→
✓
a'
→
(
●
a
⋅
◯
b0
,
●
a
⋅
◯
b1
)
~l
~>
(
●
a'
⋅
◯
b0'
,
●
a'
⋅
◯
b1'
).
Proof
.
move
=>
H
?
?
n
/=.
move
=>
[
c
]
[/=
Le
Val
]
[/=
Ha
Hb
]
/=
;
rewrite
/
op
/
cmra_op
/=
in
Ha
;
rewrite
>!(
left_id
_
_
)
in
Hb
;
rewrite
>(
left_id
_
_
)
in
Le
;
last
first
.

destruct
(
H
n
None
)
as
[
Hval'
Heq
]
=>
//.
+
eapply
cmra_validN_includedN
;
eauto
.
+
repeat
split
=>
//=.
*
rewrite
>(
left_id
_
_
).
by
apply
cmra_included_includedN
.
*
by
apply
cmra_valid_validN
.
*
simpl
in
Heq
.
by
rewrite
Heq
.

destruct
c
as
[
ac
bc
].
destruct
(
H
n
(
Some
bc
))
as
[
Hval'
Heq
]
=>
//.
+
eapply
cmra_validN_includedN
;
eauto
.
+
rewrite
!
auth_both_op
.
repeat
split
=>
//.
*
apply
cmra_included_includedN
.
by
rewrite
left_id
.
*
by
apply
cmra_valid_validN
.
*
simpl
in
*.
destruct
ac
as
[[
e
]]
=>
//
;
rewrite
/
op
/
cmra_op
/=
/
excl_op
in
Ha
;
inversion
Ha
;
by
inversion
H2
.
Qed
.
End
cmra
.
Arguments
authR
:
clear
implicits
.
...
...
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