proposition: Lemma Fadjoin_poly_eq v : v \in <<K; x>>%VS -> (Fadjoin_poly K x v).[x] = v.
proof: Proof. move/(sumv_pi_sum Fadjoin_eq_sum)=> {2}<-; rewrite horner_poly. by apply: eq_bigr => i _; rewrite inord_val mulfVK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop ssralg countalg) mathcomp(finalg zmodp matrix vector falgebra poly polydiv) mathcomp(mxpoly generic_quotient)