(**********)
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}.

Theorem rho_t_PI2 : forall t : TimeT, (rho_V * t < PI / 2)%R.