reserve i, n for Nat,
  x, y, a for Real,
  v for Element of n-tuples_on REAL,
  p, p1, p2, p3, q, q1, q2 for Point of TOP-REAL n;

theorem :: Schwartz
  |.|(p,q)|.| <= |.p.|*|.q.|
proof
  len p = n & len q = n by CARD_1:def 7;
  hence thesis by Th14;
end;
