### essai en faisant alle plus loin BCRT et WCRT. devrait etre faux

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 ... ... @@ -33,7 +33,7 @@ Section Tasks. arrives_in arr_seq j -> job_task j = tsk -> ( completed_by sched j t -> completed_by sched j (t+R) -> ~ job_response_time_bound sched j R ). ... ... @@ -44,13 +44,13 @@ Section Tasks. arrives_in arr_seq j -> job_task j = tsk -> ( completed_by sched j t-> completed_by sched j (t+R)-> job_response_time_bound sched j R ) /\ ( pending sched j t -> job_arrival j >= t-R pending sched j (t+R) -> job_arrival j > t ). End Tasks. ... ... @@ -89,7 +89,7 @@ Section Proofs. unfold task_response_time_lower_bound_until_t in P. destruct (completed_by sched j (job_arrival j + BCRT)) eqn:Q. + rewrite <- Q. apply P with (t := job_arrival j + BCRT). exact in_arr_seq. apply P with (t := job_arrival j). exact in_arr_seq. exact in_task. exact Q. + trivial. ... ... @@ -114,12 +114,12 @@ Section Proofs. destruct (completed_by sched j (job_arrival j + WCRT)) eqn:Q. + trivial. + destruct (completed_by sched j (job_arrival j + WCRT).+1) eqn:E. * apply P with (t:= (job_arrival j + WCRT).+1). exact in_arr_seq. * apply P with (t:= (job_arrival j).+1). exact in_arr_seq. exact in_task. exact E. * assert (R: (job_arrival j + WCRT).+1 - WCRT <= job_arrival j). apply P with (t := (job_arrival j + WCRT).+1). * assert (R: (job_arrival j).+1 < job_arrival j). apply P with (t := (job_arrival j).+1). exact in_arr_seq. exact in_task. unfold pending. unfold has_arrived. destruct (job_arrival j <= (job_arrival j + WCRT).+1) eqn: J. unfold has_arrived. destruct (job_arrival j <= (job_arrival j).+1 + WCRT) eqn: J. -- simpl. apply/eqP. move/eqP in E. exact E. -- exfalso; ssromega. -- exfalso; ssromega. ... ... @@ -134,14 +134,14 @@ Section Proofs. destruct PS as [arrjt cpltjt]. unfold has_arrived in arrjt. unfold completed_by in cpltjt. unfold completed_by in Q. assert (cpltjt_rewritten: job_cost j > service sched j t). ssromega. assert (R: service sched j t < service sched j (job_arrival j + WCRT)). assert (cpltjt_rewritten: job_cost j > service sched j (t+WCRT)). ssromega. assert (R: service sched j (t+WCRT) < service sched j (job_arrival j + WCRT)). { apply leq_trans with (job_cost j). exact cpltjt_rewritten. apply Q. exact in_arr_seq. exact in_task. } unfold service in R. unfold service_during in R. assert (W: t <= job_arrival j + WCRT). apply jonathan.sum_to_args_leq with (F := service_at sched j). exact R. ssromega. assert (W: t < job_arrival j). apply jonathan.sum_to_args_lt with (F := service_at sched j) in R. ssromega. exact W. Qed. End Proofs. \ No newline at end of file
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