(****************************************************************************  IEEE754  :  Rpow  Laurent Thery  ***************************************************************************** Definition of an exponential function over relative numbers *)
Require Export Omega.
Require Export Digit.
(* 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.
intros e n; elim n; simpl in |- *; auto with real.
intros n0 H' m H'0.
rewrite Rmult_assoc; rewrite <- H'; auto.
Qed.

Theorem pow_lt : forall (e : R) (n : nat), (0 < e)%R -> (0 < e ^ n)%R.