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(* 02110-1301 USA                                                     *)
(****************************************************************************  IEEE754  :  Rpower  Laurent Thery  ***************************************************************************** Definition of an exponential function over relative numbers *)
(* We have already an exponential over natural number, we prove some basic properties for this function *)
simpl in |- *; auto with real.
Qed.
simpl in |- *; auto with real.
Qed.
intros e n; elim n; simpl in |- *; auto with real.
Qed.
intros e n; elim n; simpl in |- *; auto with real.
intros n0 H' m; rewrite H'; auto with real.
Qed.
Hint Resolve pow_O pow_1 pow_NR0 pow_add: real.

Theorem pow_RN_plus :
forall (e : R) (n m : nat),
e <> 0%R -> (e ^ n)%R = (e ^ (n + m) * / e ^ m)%R.