reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th7:
  for x1,x2 being complex-valued FinSequence st len x1=len x2 holds
  len (x1-x2)=len x1
proof
  let x1,x2 be complex-valued FinSequence;
  set n=len x1;
A1: x2 is FinSequence of COMPLEX by Lm2;
  x1 is FinSequence of COMPLEX by Lm2; then
  reconsider z1=x1 as Element of (len x1)-tuples_on COMPLEX by FINSEQ_2:92;
  assume len x1=len x2; then
  reconsider z2=x2 as Element of n-tuples_on COMPLEX by A1,FINSEQ_2:92;
  dom (z1-z2)=Seg n by FINSEQ_2:124;
  hence thesis by FINSEQ_1:def 3;
end;
