Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
R
rtproofs
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
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
Sophie Quinton
rtproofs
Commits
58d8d0ab
Commit
58d8d0ab
authored
Sep 20, 2018
by
Sergey Bozhko
Committed by
Sergey Bozhko
Apr 05, 2019
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Add lemmas about arrivals_between
parent
83918615
Changes
2
Hide whitespace changes
Inline
Sidebyside
Showing
2 changed files
with
31 additions
and
24 deletions
+31
24
model/arrival/basic/arrival_sequence.v
model/arrival/basic/arrival_sequence.v
+11
22
model/arrival/basic/task_arrival.v
model/arrival/basic/task_arrival.v
+20
2
No files found.
model/arrival/basic/arrival_sequence.v
View file @
58d8d0ab
...
...
@@ 110,6 +110,16 @@ Module ArrivalSequence.
(* First, we show that the set of arriving jobs can be split
into disjoint intervals. *)
Lemma
job_arrived_between_cat
:
forall
t1
t
t2
,
t1
<=
t
>
t
<=
t2
>
jobs_arrived_between
t1
t2
=
jobs_arrived_between
t1
t
++
jobs_arrived_between
t
t2
.
Proof
.
unfold
jobs_arrived_between
;
intros
t1
t
t2
GE
LE
.
by
rewrite
(@
big_cat_nat
_
_
_
t
).
Qed
.
Lemma
jobs_arrived_between_mem_cat
:
forall
j
t1
t
t2
,
t1
<=
t
>
...
...
@@ 117,28 +127,7 @@ Module ArrivalSequence.
j
\
in
jobs_arrived_between
t1
t2
=
(
j
\
in
jobs_arrived_between
t1
t
++
jobs_arrived_between
t
t2
).
Proof
.
unfold
jobs_arrived_between
;
intros
j
t1
t
t2
GE
LE
.
apply
/
idP
/
idP
.
{
intros
IN
.
apply
mem_bigcat_nat_exists
in
IN
;
move
:
IN
=>
[
arr
[
IN
/
andP
[
GE1
LT2
]]].
rewrite
mem_cat
;
apply
/
orP
.
by
destruct
(
ltnP
arr
t
)
;
[
left

right
]
;
apply
mem_bigcat_nat
with
(
j
:
=
arr
)
;
try
(
by
apply
/
andP
;
split
).
}
{
rewrite
mem_cat
;
move
=>
/
orP
[
LEFT

RIGHT
].
{
apply
mem_bigcat_nat_exists
in
LEFT
;
move
:
LEFT
=>
[
t0
[
IN0
/
andP
[
GE0
LT0
]]].
apply
mem_bigcat_nat
with
(
j
:
=
t0
)
;
last
by
done
.
by
rewrite
GE0
/=
;
apply
:
(
leq_trans
LT0
).
}
{
apply
mem_bigcat_nat_exists
in
RIGHT
;
move
:
RIGHT
=>
[
t0
[
IN0
/
andP
[
GE0
LT0
]]].
apply
mem_bigcat_nat
with
(
j
:
=
t0
)
;
last
by
done
.
by
rewrite
LT0
andbT
;
apply
:
(
leq_trans
_
GE0
).
}
}
by
intros
j
t1
t
t2
GE
LE
;
rewrite
(
job_arrived_between_cat
_
t
).
Qed
.
Lemma
jobs_arrived_between_sub
:
...
...
model/arrival/basic/task_arrival.v
View file @
58d8d0ab
Require
Import
rt
.
util
.
all
.
Require
Import
rt
.
model
.
arrival
.
basic
.
arrival_sequence
rt
.
model
.
arrival
.
basic
.
task
rt
.
model
.
arrival
.
basic
.
job
.
From
mathcomp
Require
Import
ssreflect
ssrbool
eqtype
ssrnat
seq
path
.
From
mathcomp
Require
Import
ssreflect
ssrbool
eqtype
ssrnat
seq
path
bigop
.
(* Properties of job arrival. *)
Module
TaskArrival
.
...
...
@@ 59,6 +59,24 @@ Module TaskArrival.
Definition
num_arrivals_of_task
(
t1
t2
:
time
)
:
=
size
(
arrivals_of_task_between
t1
t2
).
(* In this section we prove some basic lemmas about number of arrivals of task. *)
Section
Lemmas
.
(* We show that the number of arrivals of task can be split into disjoint intervals. *)
Lemma
num_arrivals_of_task_cat
:
forall
t
t1
t2
,
t1
<=
t
<=
t2
>
num_arrivals_of_task
t1
t2
=
num_arrivals_of_task
t1
t
+
num_arrivals_of_task
t
t2
.
Proof
.
move
=>
t
t1
t2
/
andP
[
GE
LE
].
rewrite
/
num_arrivals_of_task
/
arrivals_of_task_between
/
arrivals_between
/
jobs_arrived_between
.
rewrite
(@
big_cat_nat
_
_
_
t
)
//=.
by
rewrite
filter_cat
size_cat
.
Qed
.
End
Lemmas
.
End
NumberOfArrivals
.
(* In this section, we prove some basic results regarding the
...
...
@@ 72,7 +90,7 @@ Module TaskArrival.
Variable
job_arrival
:
Job
>
time
.
Variable
job_task
:
Job
>
Task
.
(* Consider any arrival sequence with consistent,
duplicatefre
e arrivals, ... *)
(* Consider any arrival sequence with consistent,
nonduplicat
e arrivals, ... *)
Variable
arr_seq
:
arrival_sequence
Job
.
Hypothesis
H_consistent_arrivals
:
arrival_times_are_consistent
job_arrival
arr_seq
.
Hypothesis
H_no_duplicate_arrivals
:
arrival_sequence_is_a_set
arr_seq
.
...
...
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