fact: Definition tan prec xi := match xi with | Ibnd xl xu => if F'.le' xu xl then T.tan_fast prec xl else let pi2 := F.mul_DN prec (lower (T.pi4 prec)) c2 in match F'.lt' (F.neg pi2) xl, F'.lt' xu pi2 with | true, true => bnd (lower (T.tan_fast prec xl)) (upper (T.tan_fast prec xu)) | _, _ => Inan end | Inan => Inan end.
imports: Coq(Reals Psatz) Xreal Basic Sig Interval Float Transcend