Definition frame_tan y : {x | 0 < x < PI/2 /\ Rabs y < tan x}.

(* Specifications: *)
Lemma ub_opp : forall x, x < PI/2 -> -PI/2 < -x.
Lemma pos_opp_lt : forall x, 0 < x -> -x < x.
Lemma tech_opp_tan : forall x y, -tan x < y -> tan (-x) < y.