#[deprecated(since="8.16",note="Use Rinv_div.")]
Notation Rinv_Rdiv := Rinv_Rdiv_depr.

(* Specifications: *)
Theorem Dln : forall y:R, 0 < y -> D_in ln Rinv (fun x:R => 0 < x) y.
Lemma derivable_pt_lim_ln : forall x:R, 0 < x -> derivable_pt_lim ln x (/ x).
Theorem D_in_imp : forall (f g:R -> R) (D D1:R -> Prop) (x:R), (forall x:R, D1 x -> D x) -> D_in f g D x -> D_in f g D1 x.
Theorem D_in_ext : forall (f g h:R -> R) (D:R -> Prop) (x:R), f x = g x -> D_in h f D x -> D_in h g D x.
Theorem Dpower : forall y z:R, 0 < y -> D_in (fun x:R => Rpower x z) (fun x:R => z * Rpower x (z - 1)) ( fun x:R => 0 < x) y.
Theorem derivable_pt_lim_power : forall x y:R, 0 < x -> derivable_pt_lim (fun x => Rpower x y) x (y * Rpower x (y - 1)).
Lemma Rpower_mult_distr : forall x y z, 0 < x -> 0 < y -> Rpower x z * Rpower y z = Rpower (x * y) z.
Lemma Rlt_Rpower_l a b c: 0 < c -> 0 < a < b -> Rpower a c < Rpower b c.
Lemma Rle_Rpower_l a b c: 0 <= c -> 0 < a <= b -> Rpower a c <= Rpower b c.