
theorem LMGSEQ16:
  for D be non empty set, x1,x2,x3,x4,x5,x6,x7,x8 be Element of (4-tuples_on D)
  holds <* x1^x5,x2^x6,x3^x7,x4^x8 *> is
  Element of 4-tuples_on (8-tuples_on D)
proof
  let D be non empty set,
  x1,x2,x3,x4,x5,x6,x7,x8 be Element of (4-tuples_on D);
X1: D c= D;
  then
P1: x1^x5 is Element of 8-tuples_on D by FINSEQ_2:109;
P2: x2^x6 is Element of 8-tuples_on D by X1,FINSEQ_2:109;
P3: x3^x7 is Element of 8-tuples_on D by X1,FINSEQ_2:109;
  x4^x8 is Element of 8-tuples_on D by X1,FINSEQ_2:109;
  hence thesis by P1,P2,P3,LMGSEQ4;
end;
