Commit c6e45848 authored by Felipe Cerqueira's avatar Felipe Cerqueira
Browse files

Add lemma: completed -> not scheduled

parent 3d0bded1
......@@ -266,8 +266,25 @@ Module Schedule.
by apply leq_trans with (n := service sched j t);
[by rewrite COMPt | by apply extend_sum].
Qed.
(* Also, the service received by job j in any interval is no larger than its cost. *)
(* A completed job cannot be scheduled. *)
Lemma completed_implies_not_scheduled :
forall t,
completed job_cost sched j t ->
~~ scheduled sched j t.
Proof.
rename H_completed_jobs into COMP.
unfold completed_jobs_dont_execute in *.
intros t COMPLETED.
apply/negP; red; intro SCHED.
have BUG := COMP j t.+1.
rewrite leqNgt in BUG; move: BUG => /negP BUG; apply BUG.
unfold service; rewrite big_nat_recr // /= -addn1.
apply leq_add; first by move: COMPLETED => /eqP [<-].
by rewrite lt0n -not_scheduled_no_service negbK.
Qed.
(* The service received by job j in any interval is no larger than its cost. *)
Lemma cumulative_service_le_job_cost :
forall t t',
service_during sched j t t' <= job_cost j.
......
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