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 Th46:
  (z (#) Cseq) * seq = z * (Cseq * seq)
proof
  now
    let n be Element of NAT;
    thus ((z (#) Cseq) * seq).n = (z (#) Cseq).n * seq.n by Def8
      .= (z* Cseq.n) * seq.n by VALUED_1:6
      .= z * (Cseq.n * seq.n) by CLVECT_1:def 4
      .= z * (Cseq * seq).n by Def8
      .= (z * (Cseq * seq)).n by CLVECT_1:def 14;
  end;
  hence thesis by FUNCT_2:63;
end;
