(** ** Definition and derivative of power function with natural number exponent *)

Definition pow_fct (n:nat) (y:R) : R := y ^ n.

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.