Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
Iris
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
116
Issues
116
List
Boards
Labels
Service Desk
Milestones
Merge Requests
20
Merge Requests
20
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
Iris
Commits
563ed428
Commit
563ed428
authored
Feb 13, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
prove that we can always own an empty fragment of auth
parent
7905c004
Changes
3
Hide whitespace changes
Inline
Side-by-side
Showing
3 changed files
with
17 additions
and
4 deletions
+17
-4
algebra/cmra.v
algebra/cmra.v
+2
-0
program_logic/auth.v
program_logic/auth.v
+4
-0
program_logic/ghost_ownership.v
program_logic/ghost_ownership.v
+11
-4
No files found.
algebra/cmra.v
View file @
563ed428
...
...
@@ -378,6 +378,8 @@ Lemma cmra_update_op x1 x2 y1 y2 : x1 ~~> y1 → x2 ~~> y2 → x1 ⋅ x2 ~~> y1
Proof
.
rewrite
!
cmra_update_updateP
;
eauto
using
cmra_updateP_op
with
congruence
.
Qed
.
Lemma
cmra_update_id
x
:
x
~~>
x
.
Proof
.
intro
.
auto
.
Qed
.
Section
identity_updates
.
Context
`
{
Empty
A
,
!
CMRAIdentity
A
}.
...
...
program_logic/auth.v
View file @
563ed428
...
...
@@ -35,6 +35,10 @@ Section auth.
by
rewrite
always_and_sep_l
.
Qed
.
Lemma
auth_empty
γ
E
:
True
⊑
pvs
E
E
(
auth_own
γ
∅
).
Proof
.
by
rewrite
own_update_empty
/
auth_own
.
Qed
.
Context
{
H
φ
:
∀
n
,
Proper
(
dist
n
==>
dist
n
)
φ
}.
Lemma
auth_opened
E
a
γ
:
...
...
program_logic/ghost_ownership.v
View file @
563ed428
...
...
@@ -93,7 +93,7 @@ Proof.
by
rewrite
-(
exist_intro
γ
).
Qed
.
Lemma
own_updateP
γ
a
P
E
:
Lemma
own_updateP
P
γ
a
E
:
a
~~>
:
P
→
own
i
γ
a
⊑
pvs
E
E
(
∃
a'
,
■
P
a'
∧
own
i
γ
a'
).
Proof
.
intros
Ha
.
...
...
@@ -105,7 +105,7 @@ Proof.
rewrite
-(
exist_intro
a'
).
by
apply
and_intro
;
[
apply
const_intro
|].
Qed
.
Lemma
own_updateP_empty
`
{
Empty
A
,
!
CMRAIdentity
A
}
γ
a
P
E
:
Lemma
own_updateP_empty
`
{
Empty
A
,
!
CMRAIdentity
A
}
P
γ
E
:
∅
~~>
:
P
→
True
⊑
pvs
E
E
(
∃
a
,
■
P
a
∧
own
i
γ
a
).
Proof
.
intros
Hemp
.
...
...
@@ -119,7 +119,14 @@ Qed.
Lemma
own_update
γ
a
a'
E
:
a
~~>
a'
→
own
i
γ
a
⊑
pvs
E
E
(
own
i
γ
a'
).
Proof
.
intros
;
rewrite
(
own_updateP
_
_
(
a'
=))
;
last
by
apply
cmra_update_updateP
.
by
apply
pvs_mono
,
uPred
.
exist_elim
=>
m''
;
apply
uPred
.
const_elim_l
=>
->.
intros
;
rewrite
(
own_updateP
(
a'
=))
;
last
by
apply
cmra_update_updateP
.
by
apply
pvs_mono
,
exist_elim
=>
a''
;
apply
const_elim_l
=>
->.
Qed
.
Lemma
own_update_empty
`
{
Empty
A
,
!
CMRAIdentity
A
}
γ
E
:
True
⊑
pvs
E
E
(
own
i
γ
∅
).
Proof
.
rewrite
(
own_updateP_empty
(
∅
=))
;
last
by
apply
cmra_updateP_id
.
apply
pvs_mono
,
exist_elim
=>
a
.
by
apply
const_elim_l
=>->.
Qed
.
End
global
.
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment