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;
A1: |(x, x)| + |(x, y)| + |(x, y)| = |(x, x)| + 2*|(x, y)|;
  assume len x=len y;
  hence thesis by A1,Th126;
end;
