reserve f for Function;
reserve n,k,n1 for Nat;
reserve r,p for Real;
reserve x,y,z for object;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Real_Sequence;

theorem Th14:
  (seq1 (#) seq2) (#) seq3 = seq1 (#) (seq2 (#) seq3)
proof
  now
    let n be Element of NAT;
    thus ((seq1(#)seq2)(#)seq3).n=(seq1(#)seq2).n*seq3.n by Th8
      .=seq1.n*seq2.n*seq3.n by Th8
      .=seq1.n*(seq2.n*seq3.n)
      .=seq1.n*(seq2(#)seq3).n by Th8
      .=(seq1(#)(seq2(#)seq3)).n by Th8;
  end;
  hence thesis by FUNCT_2:63;
end;
