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(* 02110-1301 USA                                                     *)
Section alpha_no_conflict.
Unset Standard Proposition Elimination Names.
Variable intr : Trajectory.
Variable evad : EvaderTrajectory.
Variable T : TimeT.
Definition Alpha (a : R) : bool :=
let a1 :=
((Rsqr (ve evad * T) + Rsqr (l intr evad T) - Rsqr AlertRange) /
(2 * ve evad * T))%R in
let a2 := (l intr evad T * cos a)%R in
match Rle_dec a1 a2 with
| left _ => true
| right _ => false
end.

Lemma Alpha_d_AlertRange_0 :
Alpha (beta intr evad T) = true -> (d intr evad <= AlertRange)%R.