reserve i,j for Nat;

theorem
  for F being FinSequence of REAL holds 0*(len F) -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;
  (n|->(0 qua Real)) - R = -R by RVSUM_1:33;
  hence thesis by EUCLID:def 4;
end;
