Qed.
(**********)
Definition Bx_R (intruder evader : State) : R :=
(-2 * (yt evader * sind (heading intruder) * intruderSpeed) +
2 * (yt intruder * sind (heading intruder) * intruderSpeed) -
2 * (cosd (heading intruder) * xt evader * intruderSpeed) +
2 * (cosd (heading intruder) * xt intruder * intruderSpeed) +
2 * (xt evader * evaderSpeed) - 2 * (xt intruder * evaderSpeed))%R.
Definition C_R (intruder evader : State) : R :=
(Rsqr (yt intruder - yt evader) + Rsqr (xt intruder - xt evader))%R.

(* Specifications: *)
(**********)
Lemma Rsqr_R :
forall (intruder evader : State) (t : R),
Rsqr (RR intruder evader t) =
(Ax2_R intruder * Rsqr t + Bx_R intruder evader * t + C_R intruder evader)%R.