proposition: Lemma nth_mulCl c p q i : nth (mul tt (c :: p) q) i.+1 = (c * nth q i.+1 + nth (mul tt p q) i)%R.
proof: Proof. by rewrite !nth_mul' big_nat_recl. 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