proposition: Lemma centvP u V : reflect {in V, forall v, u * v = v * u} (u \in 'C(V))%VS.
proof: Proof. apply: (iffP subv_bigcapP) => [cVu y /coord_vbasis-> | cVu i _]. apply/esym/cent1vP/rpred_sum=> i _; apply: rpredZ. by rewrite -tnth_nth cent1vC memvE cVu. exact/cent1vP/cVu/vbasis_mem/mem_tnth. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop ssralg) mathcomp(finalg zmodp matrix vector poly)