intro; unfold xp in |- *; ring.
Qed.

Lemma ypt_yp0 :
forall t : R,
(yp t - yp 0)%R =
(- sin (thetat intr 0) * (xi intr t - xi intr 0) +
cos (thetat intr 0) * (yi intr t - yi intr 0))%R.