proposition: Lemma dc_delta_gt : forall j i A B, (j < i)%nat -> forall k, (k < i - j)%nat -> de_casteljau A B (delta i) j k = 0.
proof: Proof. elim=> [| j ihj] i A B hltji k hltkd /=. by move: hltkd; rewrite subn0 ltn_neqAle /delta eq_sym; case/andP; move/negPf->. have ltij : (j < i)%nat by apply: ltn_trans hltji; rewrite ltnSn. rewrite !ihj // ?mulr0 ?addr0 //; first by rewrite -subnSK. by apply: ltn_trans hltkd _; rewrite -[(i - j)%nat]subnSK. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat binomial seq choice order) mathcomp(fintype bigop ssralg poly ssrnum ssrint rat ssrnum) mathcomp(polyrcf qe_rcf_th realalg) pol poly_normal desc