(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Local Open Scope R_scope.
(** Tools *)
Definition pos_half_prf : 0 < /2.
(* The following lemmas are general purpose lemmas about squares. They do not belong here *)
(** * Properties of tangent *)
(** Proof that tangent is a bijection *)
(* to be removed? *)
(* end hide *)
(* The following lemmas about PI should probably be in Rtrigo. *)

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}.