reserve

  k,n,m,i,j for Element of NAT,
  K for Field;
reserve L for non empty addLoopStr;

theorem Th1:
  for x being FinSequence of L holds x is Element of (len x)
  -tuples_on the carrier of L
proof
  let x be FinSequence of L;
  x is Element of (the carrier of L)* by FINSEQ_1:def 11;
  then x in { s where s is Element of (the carrier of L)*: len s = len x };
  hence thesis by FINSEQ_2:def 4;
end;
