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 NORMSP_1:def 4
      .= seq.n by RLVECT_1:13;
  end;
  hence thesis by FUNCT_2:63;
end;
