(** * Square root function *)

(* Specifications: *)
Lemma filterlim_sqrt_p : filterlim sqrt (Rbar_locally' p_infty) (Rbar_locally p_infty).
Lemma is_lim_sqrt_p (f : R -> R) (x : Rbar) :
is_lim f x p_infty
-> is_lim (fun x => sqrt (f x)) x p_infty.
Lemma filterdiff_sqrt (x : R) :
0 < x -> filterdiff sqrt (locally x) (fun y => scal y (/ (2 * sqrt x))).
Lemma is_derive_sqrt (f : R -> R) (x df : R) :
is_derive f x df -> 0 < f x
-> is_derive (fun x => sqrt (f x)) x (df / (2 * sqrt (f x))).