elim a; intro.
right; red in |- *; intro; rewrite H in a0; elim (Rlt_irrefl r2 a0).
left; assumption.
right; red in |- *; intro.
rewrite H in b; elim (Rlt_irrefl r2 b).
Qed.
(***********)
Definition tau (intruder evader : State) (t : R) : R :=
match Req_EM_var (div_tau intruder evader) 0 with
| left _ => 0%R
| right _ =>
(-
(dx intruder evader t * dxdt intruder +
dy intruder evader t * dydt intruder) / div_tau intruder evader)%R
end.
Definition tmin (intruder evader : State) : R :=
match Req_EM_var (div_tau intruder evader) 0 with
| left _ => 0%R
| right _ =>
(-
(dxdt intruder * (xt intruder - xt evader) +
dydt intruder * (yt intruder - yt evader)) /
div_tau intruder evader)%R
end.

(**********)
Lemma tau_tmin :
forall (intruder evader : State) (t : R),
div_tau intruder evader <> 0%R ->
tau intruder evader t = (tmin intruder evader - t)%R.