intros; generalize (xpt t H H0); intro; generalize (xp0_pos H1); intro;
unfold hx in H2;
generalize
(Rplus_le_compat_r (xp 0) (r_vi * sin (rho_vi * t)) (xp t - xp 0) H2);
unfold Rminus in |- *; repeat rewrite Rplus_assoc;
rewrite Rplus_opp_l; rewrite Rplus_0_r; intro;
apply (plus_le_is_le (r_vi * sin (rho_vi * t)) (xp 0) (xp t) H3 H4).
Qed.

Lemma isometric_evader :
forall t : R, Rsqr_evader_distance t = (Rsqr (xp t) + Rsqr (yp t))%R.