reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;

theorem
  for x, y being real-valued FinSequence holds sqr(x-y) = sqr(y-x)
proof
  let x, y be real-valued FinSequence;
  thus (x-y)^2 = x^2 - 2(#)(x(#)y) + y^2 by RVSUM_1:69
    .= sqr y + (- 2*mlt(x,y) + sqr x)
    .= sqr y - 2*mlt(y,x) + sqr x by RFUNCT_1:8
    .= sqr(y-x) by RVSUM_1:69;
end;
