intros; set (f := u eps).
cut (derivable_pt f t); [ intro H | apply (d_u eps t) ].
cut (derive_pt f t H = derive_pt f t (d_u eps t)); [ intro | apply pr_nu ].
reg.
Qed.

(**********)
Lemma xP_derive :
forall t : R,
derive_pt xP t (xP_derivable t) = derive_pt xi t (xi_derivable t).