Notation tan_is_inj := tan_inj (only parsing).

(* Specifications: *)
Lemma exists_atan_in_frame : forall lb ub y, lb < ub -> -PI/2 < lb -> ub < PI/2 -> tan lb < y < tan ub -> {x | lb < x < ub /\ tan x = y}.
Lemma tan_1_gt_1 : tan 1 > 1.
Lemma sin_lt_x x : 0 < x -> sin x < x.