fact: Definition multiplicity_decreases f L n := let c := ac_root (Φq f L) in let r := root_multiplicity acf c (Φq f L) in let fn := nth_pol n f L in let Ln := nth_ns n f L in let cn := nth_c n f L in let rn := root_multiplicity acf cn (Φq fn Ln) in lt_dec rn r.
imports: Utf8 QArith NPeano Sorting Misc SlopeMisc Slope_base QbarM NbarM Field2 Fpolynomial Fsummation Newton ConvexHullMisc ConvexHull PolyConvexHull NotInSegment Power_series Puiseux_series Ps_add Ps_mul Ps_div PSpolynomial Puiseux_base AlgCloCharPol CharactPolyn F1Eq PosOrder F1Prop InK1m Q_field RootHeadTail RootAnyR