proposition: Lemma mul_coeff0l p q : size p = 0 -> forall n, mul_coeff tt p q n = 0%R.
proof: Proof. move=> Hp n; rewrite mul_coeffE. rewrite big_mkord big1 // => [i Hi]. rewrite (@nth_default p); by [rewrite Rmult_0_l|rewrite Hp]. Qed.
imports: Coq(ZArith Reals) Coquelicot(Coquelicot) mathcomp.ssreflect(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype bigop) Flocq(Core) Stdlib MathComp Interval Xreal Basic_rec