proposition: Lemma lagrange_zero {R: fieldType} (s: seq R): uniq s -> lagrange_poly (zero_points s) = 0.
proof: Proof. move=> Huniq. symmetry. apply: lagrange_poly_unique. - by rewrite unzip1_zero_points. - by rewrite polyseq0. - move=> x y Hin. rewrite hornerC. by rewrite (y_in_zero_points Hin). Qed.
imports: Relational(OrderEnrichedCategory GenericRulesSimple) mathcomp(all_ssreflect all_algebra reals distr realsum ssrnat ssreflect ssrfun ssrbool ssrnum eqtype choice seq) Mon(SPropBase) Crypt(Axioms ChoiceAsOrd SubDistr Couplings UniformDistrLemmas FreeProbProg Theta_dens RulesStateProb pkg_core_definition choice_type pkg_composition pkg_rhl Package Prelude) extructures(ord fset fmap) Equations(Equations)