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_2:37  :: Schwartz
  for x,y being Element of REAL n holds |.|(x,y)|.| <= |.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_2:15;
end;
