intro.
assert (H := Dxi t).
unfold xi in H.
assert (H0 := cond_x intr t).
cut
(derive_pt (x intr) t (xi_derivable intr t) =
derive_pt (x intr) t (cond_diff (x intr) t)); [ intro | apply pr_nu ].
rewrite H1 in H.
rewrite H0 in H.
unfold vi, thetat in |- *; symmetry  in |- *; assumption.
Qed.

(* Specifications: *)
Lemma DRs_sin :
forall t : R,
(derive_pt Rs t (Rs_derivable t) * sin (alphas t) +
Rs t * cos (alphas t) * derive_pt alphas t (cond_D1 alphas t))%R =
(vi intr * sin (thetat t))%R.