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Commit 0540f45a authored by Felipe Cerqueira's avatar Felipe Cerqueira
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......@@ -66,16 +66,7 @@ Module ResponseTimeAnalysisEDF.
Section Proofs.
(* The EDF-specific bound is is monotonically increasing
with the size of the interval. *)
Lemma edf_specific_bound_monotonic :
forall tsk_other R R',
R <= R' ->
edf_specific_bound (tsk_other, R) <=
edf_specific_bound (tsk_other, R').
Proof.
admit.
Qed.
(* Proof of edf-specific bound should go here *)
End Proofs.
......
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......@@ -386,27 +386,13 @@ Lemma fun_mon_iter_mon_generic :
forall T (f: T -> T) (le: rel T)
(REFL: reflexive le)
(TRANS: transitive le)
x0 x1 x2 (LE: x1 <= x2) (MIN: le x0 (f x0))
(MON: forall x1 x2, le x1 x2 -> le (f x1) (f x2)),
x0 x1 x2 (LE: x1 <= x2)
(MIN: le x0 (f x0))
(*(LE: le x0 (iter x1 f x0))*)
(MON: forall x1 x2, le x0 x1 -> le x1 x2 -> le (f x1) (f x2)),
le (iter x1 f x0) (iter x2 f x0).
Proof.
unfold reflexive, transitive in *.
ins; revert LE; revert x2; rewrite leq_as_delta; intros delta.
induction x1; try rewrite add0n.
{
induction delta; first by apply REFL.
apply TRANS with (y := iter delta f x0); first by done.
clear IHdelta.
induction delta; first by done.
{
rewrite 2!iterS; apply MON.
apply IHdelta.
}
}
{
rewrite iterS -addn1 -addnA [1 + delta]addnC addnA addn1 iterS.
by apply MON, IHx1.
}
admit.
Qed.
(*Lemma fun_monotonic_iter_monotonic :
......
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