reserve i, j, m, n for Nat,
  z, B0 for set,
  f, x0 for real-valued FinSequence;

theorem Th46:
  for B being Subset of RealVectSpace(Seg n) st B is Basis of
  RealVectSpace(Seg n) holds card B = n
proof
  let B be Subset of RealVectSpace(Seg n);
  assume
A1: B is Basis of RealVectSpace(Seg n);
  reconsider Br=RN_Base n as Subset of RealVectSpace(Seg n) by FINSEQ_2:93;
  Br is Basis of RealVectSpace(Seg n) by Th44;
  then card Br=card B by A1,RLVECT_5:25;
  hence card B=n by Lm5;
end;
