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Definition Rsqr_Rmin (intruder evader : State) : R :=
  match Req_EM_var (Ax2_R intruder) 0 with
  | left _ => 0%R
  | right _ =>
      ((4 * Ax2_R intruder * C_R intruder evader -
        Rsqr (Bx_R intruder evader)) / (4 * Ax2_R intruder))%R
  end.

Lemma asymptotic_increase_tau : forall (intruder evader : State) (t t1 t2 : R), (tau intruder evader t <= t1)%R -> (t1 <= t2)%R -> (RR intruder evader (t + t1) <= RR intruder evader (t + t2))%R.