proposition: Lemma monalgU_eq0 x k: (<< x *g k >> == 0) = (x == 0).
proof: Proof. apply/eqP/eqP => [/(congr1 (mcoeff k))|->]; last by rewrite monalgU0. by rewrite !mcoeffsE eqxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path choice finset fintype finfun) mathcomp(tuple bigop ssralg ssrint ssrnum) xfinmap