(**********)
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}.(**********)
Record TimeT : Type := mkTimeT
  {val :> R; cond_1 : (MinT <= val)%R; cond_2 : (val <= MaxT)%R}.(**********)
Record TimeT : Type := mkTimeT
  {val :> R; cond_1 : (MinT <= val)%R; cond_2 : (val <= MaxT)%R}.(**********)
Record TimeT : Type := mkTimeT
  {val :> R; cond_1 : (MinT <= val)%R; cond_2 : (val <= MaxT)%R}.(**********)
Record TimeT : Type := mkTimeT
  {val :> R; cond_1 : (MinT <= val)%R; cond_2 : (val <= MaxT)%R}.

(* Specifications: *)
Lemma MinT_is_pos : (0 < MinT)%R.
Theorem rho_ub_t_PI2 : forall (h : TypeSpeed) (t : TimeT), (rho_ub h * t < PI / 2)%R.
Theorem rho_t_PI2 : forall t : TimeT, (rho_V * t < PI / 2)%R.
Lemma rho_t_2 : forall t : TimeT, (rho_V * t < 2)%R.
Lemma r_V_is_pos : (0 < r_V)%R.
Lemma rho_V_is_pos : (0 < rho_V)%R.
Lemma m_le : forall t1 t2 : TimeT, (t1 <= t2)%R -> (m t1 <= m t2)%R.
Lemma m_rho_ub_0 : forall t : TimeT, (m_rho_ub t <= m t)%R.
Lemma m_rho_T_pos : forall t : TimeT, (0 < m t)%R.