reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem :: EUCLID_2:35
  for x,y being Element of REAL n holds |.x+y.|^2 + |.x-y.|^2 = 2*(|.x.|
  ^2 + |.y.|^2)
proof
  let x,y be Element of REAL n;
  len x = n & len y = n by CARD_1:def 7;
  hence thesis by EUCLID_2:13;
end;
