(** In dependently typed environments it is sometimes hard to rewrite. Having pr_nu for separate x with a proof that they are equal helps. *)

Lemma pr_nu_xeq :
forall f (x1 x2:R) (pr1:derivable_pt f x1) (pr2:derivable_pt f x2),
x1 = x2 -> derive_pt f x1 pr1 = derive_pt f x2 pr2.