intro; unfold Rsqr_intruder_distance in |- *; rewrite xpt_xp0;
rewrite ypt_yp0; repeat rewrite Rsqr_plus; ring_simplify;
repeat rewrite Rsqr_mult;
rewrite <- Rsqr_neg.
pattern (Rsqr (xi intr t - xi intr 0)) at 1 in |- *.
replace (Rsqr (xi intr t - xi intr 0)) with
((Rsqr (sin (thetat intr 0)) + Rsqr (cos (thetat intr 0))) *
Rsqr (xi intr t - xi intr 0))%R.
pattern (Rsqr (yi intr t - yi intr 0)) at 1 in |- *.
replace (Rsqr (yi intr t - yi intr 0)) with
((Rsqr (sin (thetat intr 0)) + Rsqr (cos (thetat intr 0))) *
Rsqr (yi intr t - yi intr 0))%R.
ring.
rewrite sin2_cos2 in |- *;  ring.
rewrite sin2_cos2 in |- *;  ring.
Qed.

(* Specifications: *)
Lemma majoration :
forall t : R,
(Rsqr (yp t) <= Rsqr_evader_distance t)%R /\
(Rsqr (xp t) <= Rsqr_evader_distance t)%R.