proposition: Theorem zerop_1st_n_const_coeff_false_succ : ∀ f L n, (ps_poly_nth 0 f ≠ 0)%ps → zerop_1st_n_const_coeff n (nth_pol 1 f L) (nth_ns 1 f L) = false ↔ zerop_1st_n_const_coeff (S n) f L = false.
proof: Proof. intros f L n Hnz. split; intros H. apply zerop_1st_n_const_coeff_false_iff. apply not_zero_1st_prop; assumption. simpl in H. destruct (ps_zerop K (ps_poly_nth 0 f)); [ contradiction | ]. assumption. Qed.
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