proposition: Lemma gen_dim_ub_proof nA : [exists B : 'rV_nA, row_free (subbase B)] -> (nA <= n)%N.
proof: Proof. case/existsP=> B /eqnP def_nAd. by rewrite (leq_trans _ (rank_leq_col (subbase B))) // def_nAd leq_pmulr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)