Notation atan_right_inv := tan_atan (only parsing). (* compat *)

(* Specifications: *)
Lemma atan_opp : forall x,
atan (- x) = - atan x.
Lemma derivable_pt_atan : forall x,
derivable_pt atan x.
Lemma atan_increasing : forall x y,
x < y -> atan x < atan y.
Lemma atan_0 : atan 0 = 0.
Lemma atan_eq0 : forall x,
atan x = 0 -> x = 0.
Lemma atan_1 : atan 1 = PI/4.
Lemma atan_tan : forall x, - (PI / 2) < x < PI / 2 ->
atan (tan x) = x.
Lemma atan_inv : forall x, (0 < x)%R ->
atan (/ x) = (PI / 2 - atan x)%R.