(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 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.

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