(* The following lemmas are general purpose lemmas about squares. They do not belong here *)

(* Specifications: *)
Lemma pow2_ge_0 : forall x, 0 <= x^2.
Lemma pow2_abs : forall x, Rabs x^2 = x^2.
(** ** Properties of tangent *)
(** *** Derivative of tangent *)
Lemma derivable_pt_tan : forall x, -PI/2 < x < PI/2 ->
derivable_pt tan x.
Lemma derive_pt_tan : forall x,
forall (Pr1: -PI/2 < x < PI/2),
derive_pt tan x (derivable_pt_tan x Pr1) = 1 + (tan x)^2.