reserve f for Function;
reserve n,k,n1 for Element of NAT;
reserve r,p for Complex;
reserve x,y for set;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Complex_Sequence;

theorem Th8:
  (seq1(#)seq2)(#)seq3=seq1(#)(seq2(#)seq3)
proof
  now
    let n;
    thus ((seq1(#)seq2)(#)seq3).n=(seq1(#)seq2).n*seq3.n by VALUED_1:5
      .=seq1.n*seq2.n*seq3.n by VALUED_1:5
      .=seq1.n*(seq2.n*seq3.n)
      .=seq1.n*(seq2(#)seq3).n by VALUED_1:5
      .=(seq1(#)(seq2(#)seq3)).n by VALUED_1:5;
  end;
  hence thesis by FUNCT_2:63;
end;
