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

theorem Th47:
  {} is Basis of RealVectSpace(Seg 0)
proof
  consider A being finite Subset of RealVectSpace(Seg 0) such that
A1: A is Basis of RealVectSpace(Seg 0) by RLVECT_5:def 1;
  card A=0 by A1,Th46;
  then A={};
  hence thesis by A1;
end;
