fact: Definition get_bounds (prec : F.precision) (l : list I.type): F.type * F.type := let yi := match l with | cons hi l => List.fold_left I.join l hi | nil => I.empty end in let yl := I.lower yi in let yu := I.upper yi in let yw := F.sub_UP prec yu yl in (F.sub_DN prec yu yw, F.add_UP prec yl yw).
imports: Coq(Reals List) Sig Generic_proof Interval_helper Xreal Interval Tree Reify Prog