(** ** arccosine of specific values *)

(* Specifications: *)
Lemma acos_0 : acos 0 = PI/2.
Lemma acos_1 : acos 1 = 0.
Lemma acos_opp : forall x,
acos (- x) = PI - acos x.
Lemma acos_inv_sqrt2 : acos (/sqrt 2) = PI/4.
(** ** Bounds of arccosine *)
Lemma acos_bound : forall x,
0 <= acos x <= PI.
Lemma acos_bound_lt : forall x, -1 < x < 1 ->
0 < acos x < PI.