Prove that for any real characteristic function \(\varphi(t)\) the inequality

\[ 1-\varphi(2 t) \leqslant 4\{(1-\varphi(t)\} \]

holds and, hence, for any characteristic function the inequality \[ 1-|f(2 t)|^{2} \leqslant 4\left\{1-|f(t)|^{2}\right\} \]
also holds.