Definition f (x : R) : R := fab 2 2 x.

(* Specifications: *)
Lemma Signe_df : forall x, 0 < x -> sign (Derive f x) = sign (- ln x).
Lemma filterlim_f_0 : filterlim f (at_right 0) (Rbar_locally m_infty).
Lemma Lim_f_p_infty : is_lim f p_infty 0.
Lemma Variation_1 : forall x y, 0 < x -> x < y -> y < 1 -> f x < f y.
Lemma Variation_2 : forall x y, 1 < x -> x < y -> f x > f y.
Lemma f_eq_1_0_1 : exists x, 0 < x <= 1 /\ f x = 1.
Lemma f_eq_1_1_p_infty : exists x, 1 <= x /\ f x = 1.
Lemma If : forall x, 0 < x -> is_derive (fun y : R => 2 * ln y + (ln y) ^ 2) x (f x).
Lemma RInt_f : is_RInt f ( / exp 1) 1 1.