reserve

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

theorem Th20:
  for x being FinSequence of K holds |(x, 0*(K,len x))| = 0.K
proof
  let x be FinSequence of K;
  set n=len x;
  reconsider p1=x as Element of n-tuples_on (the carrier of K) by FINSEQ_2:92;
  |(x, 0*(K,n))| = Sum mlt(p1,0*(K,n)) by FVSUM_1:def 9
    .= Sum 0*(K,n) by Th13
    .= 0.K by MATRIX_3:11;
  hence thesis;
end;
