reserve X for ComplexUnitarySpace;
reserve g for Point of X;
reserve seq, seq1, seq2 for sequence of X;
reserve Rseq for Real_Sequence;
reserve Cseq,Cseq1,Cseq2 for Complex_Sequence;
reserve z,z1,z2 for Complex;
reserve r for Real;
reserve k,n,m for Nat;

theorem
  Cseq * (- seq) = (- Cseq) * seq
proof
  now
    let n be Element of NAT;
    thus (Cseq * (- seq)).n = Cseq.n * (-seq).n by Def8
      .= Cseq.n * (-(seq.n)) by BHSP_1:44
      .= (-(Cseq.n)) * seq.n by CLVECT_1:6
      .= (- Cseq).n * seq.n by VALUED_1:8
      .= ((- Cseq) * seq).n by Def8;
  end;
  hence thesis by FUNCT_2:63;
end;
