(* 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                                                     *)
Require Export pi_ineq.
(* Some usefull constants *)
Definition g : R := (322 / 10)%R.
Definition ConflictRange : R := 200%R.
Definition MinSpeed : R := 201%R.
Definition MaxSpeed : R := 880%R.
Definition MaxBank : R := (61 / 100)%R.
(**********)
Record TypeSpeed : Type := mkTypeSpeed
{v :> R; v_cond1 : (MinSpeed <= v)%R; v_cond2 : (v <= MaxSpeed)%R}.
Definition tan_lb_MaxBank : R := (6 / 10)%R.
Definition tan_ub_MaxBank : R := (7 / 10)%R.

(* Specifications: *)
(**********)
Lemma tanBank_def :
forall x : R, (- MaxBank <= x)%R -> (x <= MaxBank)%R -> cos x <> 0%R.