### removed a long proof

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 ... ... @@ -153,6 +153,28 @@ Section Prefixverif. (* --- IV --- LEMMAS --- IV --- *) (*========================================================================*) Local Lemma utilitaire: forall j j' t t', completes_at sched j t -> completes_at sched j' t' -> completed_by sched j (maxn t t'). Proof. intros j j' t t' Q R. assert (U: maxn t t' >= t). destruct (t <= t') eqn:E. assert (V: maxn t t' = t'). apply/maxn_idPr. exact E. rewrite V. exact E. assert (U': t >= t'). ssromega. assert (V: maxn t t' = t). apply/maxn_idPl. exact U'. rewrite V. apply leqnn. unfold completed_by. unfold service. unfold completes_at in Q. unfold service in Q. assert (J: service_during sched j 0 t <= service_during sched j 0 (maxn t t')). unfold service_during. unfold service_during in Q. apply sum.extend_sum. apply leqnn. exact U. apply leq_trans with (service_during sched j 0 t). ssromega. exact J. Qed. Lemma periodic_jitter_infinite: forall (tsk:Task), ( forall t, respects_periodic_jitter_task_model_up_to_t tsk t ) -> ... ... @@ -168,6 +190,7 @@ Section Prefixverif. assert (P1: correction_t tsk j (t)) by (apply P). apply P1. unfold completes_at in Q. unfold completed_by. ssromega. - intros j j'. assert (Q: exists t, completes_at sched j t). apply all_jobs_complete. destruct Q as [t Q]. ... ... @@ -176,37 +199,9 @@ Section Prefixverif. assert (P2: injection_t tsk j j' (maxn t t')) by (apply P). apply P2. + assert (U: maxn t t' >= t). destruct (t <= t') eqn:E. assert (V: maxn t t' = t'). apply/maxn_idPr. exact E. rewrite V. exact E. assert (U': t >= t'). ssromega. assert (V: maxn t t' = t). apply/maxn_idPl. exact U'. rewrite V. apply leqnn. unfold completed_by. unfold service. unfold completes_at in Q. unfold service in Q. assert (J: service_during sched j 0 t <= service_during sched j 0 (maxn t t')). unfold service_during. unfold service_during in Q. apply sum.extend_sum. apply leqnn. exact U. apply leq_trans with (service_during sched j 0 t). ssromega. exact J. + assert (U: maxn t t' >= t'). destruct (t <= t') eqn:E. assert (V: maxn t t' = t'). apply/maxn_idPr. exact E. rewrite V. apply leqnn. assert (U': t >= t'). ssromega. assert (V: maxn t t' = t). apply/maxn_idPl. exact U'. rewrite V. exact U'. unfold completed_by. unfold service. unfold completes_at in R. unfold service in R. assert (J: service_during sched j' 0 t' <= service_during sched j' 0 (maxn t t')). unfold service_during. unfold service_during in R. apply sum.extend_sum. apply leqnn. exact U. apply leq_trans with (service_during sched j' 0 t'). ssromega. exact J. + apply utilitaire with j'. exact Q. exact R. + rewrite maxnC. apply utilitaire with j. exact R. exact Q. - intro n. assert (P3: surjection_t tsk n (offset + n * period +jitter) ) by (apply P). ... ...
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