Library prosa.analysis.facts.model.sequential

Consider any type of job associated with any type of tasks...
  Context {Job: JobType}.
  Context {Task: TaskType}.
  Context `{JobTask Job Task}.

... with arrival times and costs ...
  Context `{JobArrival Job}.
  Context `{JobCost Job}.

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

Consider any arrival sequence ...
  Variable arr_seq : arrival_sequence Job.

... and any schedule of this arrival sequence ...
  Variable sched : schedule PState.

... in which the sequential tasks hypothesis holds.
A simple corollary of this hypothesis is that the scheduler executes a job with the earliest arrival time.
  Corollary scheduler_executes_job_with_earliest_arrival:
     j1 j2 t,
      arrives_in arr_seq j1
      arrives_in arr_seq j2
      same_task j1 j2
      ~~ completed_by sched j2 t
      scheduled_at sched j1 t
      job_arrival j1 job_arrival j2.

End ExecutionOrder.