Library prosa.analysis.facts.readiness.basic

Throughout this file, we assume the basic (i.e., Liu & Layland) readiness model.
Consider any kind of jobs...
  Context {Job : JobType}.

... and any kind of processor state.
  Context {PState : Type}.
  Context `{ProcessorState Job PState}.

Suppose jobs have an arrival time and a cost.
  Context `{JobArrival Job} `{JobCost Job}.

In the basic Liu & Layland model, a schedule satisfies that only ready jobs execute as long as jobs must arrive to execute and completed jobs don't execute, which we note with the following theorem.
  Lemma basic_readiness_compliance:
      jobs_must_arrive_to_execute sched
      completed_jobs_dont_execute sched
      jobs_must_be_ready_to_execute sched.
    movesched ARR COMP.
    rewrite /jobs_must_be_ready_to_executej t SCHED.
    rewrite /job_ready /basic_ready_instance /pending.
    apply /andP; split.
    - by apply ARR.
    - rewrite -less_service_than_cost_is_incomplete.
      by apply COMP.

End LiuAndLaylandReadiness.