theorem Th21:
  len b1 = dim V1
proof
  reconsider R=rng b1 as Basis of V1 by MATRLIN:def 2;
A1: b1 is one-to-one by MATRLIN:def 2;
  thus len b1 = card Seg len b1 by FINSEQ_1:57
    .= card dom b1 by FINSEQ_1:def 3
    .= card R by A1,CARD_1:70
    .= dim V1 by VECTSP_9:def 1;
end;
