proposition: Lemma basis_not0 x U X : basis_of U X -> x \in X -> x != 0.
proof: Proof. by move/basis_free/free_not0; apply. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)