proposition: Lemma horner_div_mixed_r p b x : horner tt (div_mixed_r tt p b) x = (horner tt p x / b)%R.
proof: Proof. rewrite !hornerE size_div_mixed_r /Rdiv Rmult_comm. rewrite big_endo; first last. by rewrite Rmult_0_r. by move=> *; rewrite Rmult_plus_distr_l. apply: eq_bigr => i _. by rewrite nth_div_mixed_r -Rmult_assoc; congr Rmult; rewrite Rmult_comm. 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