reserve i,j for Nat;

theorem
  for F being FinSequence of REAL holds F - 0*(len F) = F
proof
  let F be FinSequence of REAL;
  set n=len F;
  reconsider R=F as Element of n-tuples_on REAL by FINSEQ_2:92;
  R - (n|->(0 qua Real)) = R by RVSUM_1:32;
  hence thesis by EUCLID:def 4;
end;
