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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_decrease_tmin : forall (intruder evader : State) (t1 t2 : R), (t2 <= tmin intruder evader)%R -> (t1 <= t2)%R -> (RR intruder evader t2 <= RR intruder evader t1)%R.