reserve

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

theorem Th3:
  for x1,x2 being FinSequence of L st len x1=len x2 holds len (x1- x2)=len x1
proof
  let x1,x2 be FinSequence of L;
  set n=len x1;
  reconsider z1=x1 as Element of (len x1)-tuples_on (the carrier of L) by
FINSEQ_2:92;
  assume len x1=len x2;
  then reconsider z2=x2 as Element of n-tuples_on (the carrier of L) by
FINSEQ_2:92;
  dom (z1-z2)=Seg n by FINSEQ_2:124;
  hence thesis by FINSEQ_1:def 3;
end;
