Library prosa.analysis.facts.model.ideal.service_of_jobs

Throughout this file, we assume ideal uni-processor schedules.

Service Received by Sets of Jobs in Ideal Uni-Processor Schedules

In this file, we establish a fact about the service received by sets of jobs under ideal uni-processor schedule and the presence of idle times. The lemma is currently specific to ideal uniprocessors only because of the lack of a general notion of idle time, which should be added in the near future. Conceptually, the fact holds for any ideal_progress_proc_model. Once a general notion of idle time has been defined, this file should be generalized.
Section IdealModelLemmas.

Consider any type of tasks ...
  Context {Task : TaskType}.

... 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 with consistent arrivals.
Next, consider any ideal uni-processor schedule of this arrival sequence ...
... where jobs do not execute before their arrival or after completion.
Let P be any predicate over jobs.
  Variable P : pred Job.

We prove that if the total service within some time interval [t1,t2) is smaller than t2 - t1, then there is an idle time instant t [t1,t2)].