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add lemma relating task cost and task rbf

Merged Kimaya Bedarkar requested to merge RTS/internships-2021:task_rbf_lemma into master
+ 13
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@@ -272,7 +272,7 @@ Section RequestBoundFunctions.
Hypothesis H_j_arrives : arrives_in arr_seq j.
Hypothesis H_job_of_tsk : job_of_task tsk j.
(** Then we prove that [task_rbf] at [ε] is greater than or equal to task cost. *)
(** Then we prove that [task_rbf] at [ε] is greater than or equal to the task's WCET. *)
Lemma task_rbf_1_ge_task_cost:
task_rbf ε >= task_cost tsk.
Proof.
@@ -296,6 +296,18 @@ Section RequestBoundFunctions.
by rewrite CONS.
Qed.
(** As a corollary, we prove that the [task_rbf] at any point [A] greater than
[0] is no less than the task's WCET. *)
Lemma task_rbf_ge_task_cost:
forall A,
A > 0 ->
task_rbf A >= task_cost tsk.
Proof.
case => // A GEQ.
apply: (leq_trans task_rbf_1_ge_task_cost).
exact: task_rbf_monotone.
Qed.
(** Assume that [tsk] has a positive cost. *)
Hypothesis H_positive_cost : 0 < task_cost tsk.
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