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Felipe Cerqueira
rtproofs
Commits
cecba062
Commit
cecba062
authored
Sep 09, 2016
by
Felipe Cerqueira
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Remove unnecessary assumption job_cost > 0
parent
bf05f1be
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implementation/uni/basic/schedule.v
implementation/uni/basic/schedule.v
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implementation/uni/basic/schedule.v
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cecba062
...
...
@@ 63,13 +63,9 @@ Module ConcreteScheduler.
Context
{
Job
:
eqType
}
.
Variable
job_cost
:
Job
>
time
.
(
*
Let
arr_seq
be
any
job
arrival
sequence
with
no
duplicates
,
..
.
*
)
(
*
Let
arr_seq
be
any
job
arrival
sequence
with
no
duplicates
.
*
)
Variable
arr_seq
:
arrival_sequence
Job
.
Hypothesis
H_arrival_sequence_is_a_set
:
arrival_sequence_is_a_set
arr_seq
.
(
*
...
where
jobs
have
positive
cost
.
*
)
Hypothesis
H_job_cost_positive
:
forall
(
j
:
JobIn
arr_seq
),
job_cost_positive
job_cost
j
.
(
*
Consider
any
JLDP
policy
that
is
transitive
and
total
.
*
)
Variable
higher_eq_priority
:
JLDP_policy
arr_seq
.
...
...
@@ 189,7 +185,6 @@ Module ConcreteScheduler.
Theorem
scheduler_completed_jobs_dont_execute
:
completed_jobs_dont_execute
job_cost
sched
.
Proof
.
rename
H_job_cost_positive
into
GT0
.
unfold
completed_jobs_dont_execute
,
service
,
service_during
.
intros
j
t
.
induction
t
;
first
by
rewrite
big_geq
.
...
...
@@ 204,9 +199,15 @@ Module ConcreteScheduler.
rewrite
EQ
{
2
}
[
job_cost
j
]
addn0
;
apply
leq_add
;
first
by
done
.
destruct
t
.
{
rewrite
big_geq
// in EQ.
specialize
(
GT0
j
);
unfold
job_cost_positive
in
*
.
by
rewrite

EQ
ltn0
in
GT0
.
rewrite
/
service_at
/
scheduled_at
.
destruct
(
sched
0
==
Some
j
)
eqn
:
SCHED
;
last
by
done
.
move:
SCHED
=>
/
eqP
SCHED
.
rewrite
scheduler_picks_first_job
in
SCHED
.
set
jobs
:=
sorted_pending_jobs
_
_
_
_
_
in
SCHED
.
have
IN
:
j
\
in
jobs
.
by
destruct
jobs
;
last
by
move
:
SCHED
=>
/=
;
case
=>
SAME
;
subst
;
rewrite
in_cons
eq_refl
.
rewrite
mem_sort
mem_filter
in
IN
;
move
:
IN
=>
/
andP
[
/
andP
[
_
NOTCOMP
]
_
].
by
rewrite
/
completed_by

EQ
eq_refl
in
NOTCOMP
.
}
{
unfold
service_at
,
scheduled_at
.
...
...
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