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
  (-1r) * seq = - seq
proof
  now
    let n be Element of NAT;
    thus ((-1r) * seq).n = (-1r) * seq.n by CLVECT_1:def 14
      .= - seq.n by CLVECT_1:3
      .= (-seq).n by BHSP_1:44;
  end;
  hence thesis by FUNCT_2:63;
end;
