reserve D for non empty set;
reserve s for FinSequence of D;
reserve m,n for Element of NAT;

theorem Th21:
  for S be non empty set,
  x1,x2,x3,x4,x5,x6,x7,x8,
  x9,x10,x11,x12,x13,x14,x15,x16
  be Element of S holds
  ex s be FinSequence of S st
  s is 16-element &
  s.1=x1&s.2=x2&s.3=x3&s.4=x4&
  s.5=x5&s.6=x6&s.7=x7&s.8=x8&
  s.9=x9&s.10=x10&s.11=x11&s.12=x12&
  s.13=x13&s.14=x14&s.15=x15&s.16=x16
  proof
    let S be non empty set,
    x1,x2,x3,x4,x5,x6,x7,x8,
    x9,x10,x11,x12,x13,x14,x15,x16 be Element of S;
    consider a1 be FinSequence of S such that
    A1: a1 is 8-element &
    a1.1=x1&a1.2=x2&a1.3=x3&a1.4=x4&
    a1.5=x5&a1.6=x6&a1.7=x7&a1.8=x8 by Th20;
    consider a2 be FinSequence of S such that
    A2: a2 is 8-element &
    a2.1=x9&a2.2=x10&a2.3=x11&a2.4=x12&
    a2.5=x13&a2.6=x14&a2.7=x15&a2.8=x16 by Th20;
     reconsider a1,a2 as 8-element FinSequence of S by A1,A2;
    take a1^a2;
    thus a1^a2 is 16-element;
A3:   (a1^a2).1 = a1.1 & ... & (a1^a2).8 = a1.8 by FINSEQ_3:154;
     (a1^a2).(8+1) = a2.1 & ... & (a1^a2).(8+8) = a2.8
       by FINSEQ_3:155;
   hence thesis by A3,A1,A2;
  end;
