Library prosa.analysis.facts.preemption.job.preemptive

Require Export prosa.model.task.preemption.parameters.

Furthermore, we assume the fully preemptive job model.
Require Import prosa.model.preemption.fully_preemptive.

Preemptions in Fully Preemptive Model

In this section, we prove that instantiation of predicate job_preemptable to the fully preemptive model indeed defines a valid preemption model.
Section FullyPreemptiveModel.

Consider any type of jobs.
  Context {Job : JobType}.
  Context `{JobArrival Job}.
  Context `{JobCost Job}.

Consider any kind of processor state model, ...
  Context {PState : Type}.
  Context `{ProcessorState Job PState}.

... any job arrival sequence, ...
  Variable arr_seq : arrival_sequence Job.

... and any given schedule.
  Variable sched : schedule PState.

Then, we prove that fully_preemptive_model is a valid preemption model.
  Lemma valid_fully_preemptive_model:
    valid_preemption_model arr_seq sched.

We also prove that under the fully preemptive model job_max_nonpreemptive_segment j is equal to 0, when job_cost j = 0 ...
  Lemma job_max_nps_is_0:
    ∀ j,
      job_cost j = 0 →
      job_max_nonpreemptive_segment j = 0.

... or ε when job_cost j > 0.
  Lemma job_max_nps_is_ε:
    ∀ j,
      job_cost j > 0 →
      job_max_nonpreemptive_segment j = ε.

End FullyPreemptiveModel.
Hint Resolve valid_fully_preemptive_model : basic_facts.