reserve i,j for Nat;

theorem
  for F1,F2 being FinSequence of REAL st len F1=len F2 & F1 - F2 = 0*(
  len F1) holds F1=F2
proof
  let F1,F2 be FinSequence of REAL;
  set n=len F1;
  assume len F1=len F2;
  then reconsider R1=F1, R2=F2 as Element of n-tuples_on REAL by FINSEQ_2:92;
  R1 - R2 = (n|->0) implies R1 = R2 by RVSUM_1:38;
  hence thesis by EUCLID:def 4;
end;
