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(** * Definition of arctangent                           *)
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(** ** Definition of arctangent as the reciprocal function of tangent and proof of this status *)

Lemma pos_opp_lt : forall x, 0 < x -> -x < x.
Definition pre_atan (y : R) : {x : R | -PI/2 < x < PI/2 /\ tan x = y}.