theorem Th119:
  for x being real-valued FinSequence holds |(x,x)| >= 0
proof
  let x be real-valued FinSequence;
  set n=len x;
  x is FinSequence of REAL by Lm2;
  then reconsider w = x as Element of n-tuples_on REAL by FINSEQ_2:92;
  |(x, x)| = Sum sqr(w);
  hence thesis by Th86;
end;
