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

theorem
  for B being Orthogonal_Basis of n holds card B = n
proof
  let B be Orthogonal_Basis of n;
  reconsider B0=B as Subset of RealVectSpace(Seg n) by FINSEQ_2:93;
  B0 is Basis of RealVectSpace(Seg n) by Th49;
  hence card B = n by Th46;
end;
