 Theorem. Suppose that \(\Bel\) is deductively cogent and \(\langle \Bel, \Pr \rangle\) satisfy \(\text{WLT}^{\Pr(\cap \Bel)}\). Then, \(\langle \Bel, \Pr \rangle\) satsify \(\text{HT}^{\frac{1}{2}}\) and \(\varnothing \notin \Bel\).