Library rt.restructuring.analysis.facts.edf

Require Import rt.restructuring.model.priority.edf.
Require Import rt.restructuring.model.task.absolute_deadline.

In this section, we prove a few properties about EDF policy.
Section PropertiesOfEDF.

Consider any type of tasks with relative deadlines ...
  Context {Task : TaskType}.
  Context `{TaskDeadline Task}.

... and any type of jobs associated with these tasks.
  Context {Job : JobType}.
  Context `{JobTask Job Task}.
  Context `{JobArrival Job}.
  Context `{JobCost Job}.

Consider any arrival sequence.
  Variable arr_seq : arrival_sequence Job.

EDF respects sequential tasks hypothesis.
  Lemma EDF_respects_sequential_tasks:
    policy_respects_sequential_tasks.
  Proof.
    intros TSK ARR.
    move: TSK ā‡’ /eqP TSK.
    unfold hep_job, EDF, job_deadline, job_deadline_from_task_deadline; rewrite TSK.
      by rewrite leq_add2r.
  Qed.

End PropertiesOfEDF.

We add the above lemma into a "Hint Database" basic_facts, so Coq will be able to apply them automatically.
Hint Resolve
     EDF_respects_sequential_tasks : basic_facts.