reserve X for non empty CUNITSTR;
reserve a, b for Complex;
reserve x, y for Point of X;
reserve X for ComplexUnitarySpace;
reserve x, y, z, u, v for Point of X;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve  n for Nat;

theorem
  seq = seq + 0.X
proof
  now
    let n be Element of NAT;
    thus (seq + 09(X)).n = seq.n + 09(X) by BHSP_1:def 6
      .= seq.n by RLVECT_1:4;
  end;
  hence thesis by FUNCT_2:63;
end;
