theorem Th116:
  for x1,x2 being real-valued FinSequence st len x1=len x2 holds
  len (x1-x2)=len x1
proof
  let x1,x2 be real-valued FinSequence;
  set n=len x1;
A1: x2 is FinSequence of REAL by Lm2;
  x1 is FinSequence of REAL by Lm2;
  then reconsider z1=x1 as Element of (len x1)-tuples_on REAL by FINSEQ_2:92;
  assume len x1=len x2;
  then reconsider z2=x2 as Element of n-tuples_on REAL by A1,FINSEQ_2:92;
  dom (z1-z2)=Seg n by FINSEQ_2:124;
  hence thesis by FINSEQ_1:def 3;
end;
