Section constants.
Variable intr : Trajectory.
Variable evad : EvaderTrajectory.
unfold MinSpeed in |- *; left; prove_sup.
Qed.
unfold MaxSpeed in |- *; left; prove_sup.
Qed.
(**********)
Definition V : TypeSpeed := mkTypeSpeed 250 Rle_201_250 Rle_250_880.
Definition r_V : R := r V.
Definition rho_V : R := rho V.
Definition AlertTime : R := 19%R.
Definition AlertRange : R := 1400%R.
Definition tstep : R := (/ 2)%R.
Definition MaxStep : R := 1%R.
Definition MaxT : R := 10%R.
Definition MinT : R := (MaxT - tstep)%R.
Definition m (t : R) : R :=
let z := IZR 2 in (z * r_V * sin (rho_V * (t / z)))%R.
Definition m_rho_ub (t : R) : R :=
let z := IZR 2 in (z * r_lb V * sin_lb (rho_lb V * (t / z)))%R.
(**********)
Record TimeT : Type := mkTimeT
{val :> R; cond_1 : (MinT <= val)%R; cond_2 : (val <= MaxT)%R}.
Proof with trivial.
unfold MinT in |- *; unfold MaxT, tstep in |- *;
apply Rmult_lt_reg_l with 2%R...
prove_sup...
rewrite Rmult_0_r; rewrite Rmult_minus_distr_l; rewrite <- Rinv_r_sym...
apply Rlt_trans with 1%R; prove_sup...
Qed.

(**********)
Theorem rho_ub_t_PI2 :
forall (h : TypeSpeed) (t : TimeT), (rho_ub h * t < PI / 2)%R.