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Björn Brandenburg
prosa
Commits
a77c7c71
Commit
a77c7c71
authored
Apr 01, 2020
by
Björn Brandenburg
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additional minor lemmas on job arrivals
parent
93b40629
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analysis/facts/behavior/arrivals.v
analysis/facts/behavior/arrivals.v
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analysis/facts/behavior/arrivals.v
View file @
a77c7c71
...
...
@@ -3,6 +3,37 @@ Require Export prosa.util.all.
(** * Arrival Sequence *)
(** First, we relate the stronger to the weaker arrival predicates. *)
Section
ArrivalPredicates
.
(** Consider any kinds of jobs with arrival times. *)
Context
{
Job
:
JobType
}
`
{
JobArrival
Job
}.
(** A job that arrives in some interval <<[t1, t2)>> certainly arrives before
time [t2]. *)
Lemma
arrived_between_before
:
forall
j
t1
t2
,
arrived_between
j
t1
t2
->
arrived_before
j
t2
.
Proof
.
move
=>
j
t1
t2
.
now
rewrite
/
arrived_before
/
arrived_between
=>
/
andP
[
_
CLAIM
].
Qed
.
(** A job that arrives before a time [t] certainly has arrived by time
[t]. *)
Lemma
arrived_before_has_arrived
:
forall
j
t
,
arrived_before
j
t
->
has_arrived
j
t
.
Proof
.
move
=>
j
t
.
rewrite
/
arrived_before
/
has_arrived
.
now
apply
ltnW
.
Qed
.
End
ArrivalPredicates
.
(** In this section, we relate job readiness to [has_arrived]. *)
Section
Arrived
.
...
...
@@ -51,6 +82,16 @@ Section Arrived.
by
apply
ready_implies_arrived
.
Qed
.
(** Since backlogged jobs are by definition ready, any backlogged job must have arrived. *)
Corollary
backlogged_implies_arrived
:
forall
j
t
,
backlogged
sched
j
t
->
has_arrived
j
t
.
Proof
.
rewrite
/
backlogged
.
move
=>
j
t
/
andP
[
READY
_
].
now
apply
ready_implies_arrived
.
Qed
.
End
Arrived
.
(** In this section, we establish useful facts about arrival sequence prefixes. *)
...
...
@@ -199,4 +240,4 @@ Section ArrivalSequencePrefix.
End
ArrivalTimes
.
End
ArrivalSequencePrefix
.
\ No newline at end of file
End
ArrivalSequencePrefix
.
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