theorem
  for x,y being real-valued FinSequence st len x=len y holds |(x-y, x-
  y)| = |(x, x)| - 2*|(x, y)| + |(y, y)|
proof
  let x,y be real-valued FinSequence;
  assume len x=len y;
  then |(x-y, x-y)| = |(x,x)| - |(x,y)| - |(y,x)| + |(y, y)| by Th127
    .= |(x,x)| - 2*|(x,y)| + |(y, y)|;
  hence thesis;
end;
