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_2:36
  for x,y being Element of REAL n holds |.x+y.|^2 - |.x-y.|^2 = 4* |(x,y )|
proof
  let x,y be Element of REAL n;
  len x = n & len y = n by CARD_1:def 7;
  hence thesis by EUCLID_2:14;
end;
