A direct proof of the theorem is given in this paper.

本文给出了该定理的一个直接证明。

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However, in this case we can simplify things quite a bit and just show a direct proof by leveraging our first proof.

不过，在本例中，我们可以进行相当程度的简化，只是通过补充我们的第一个证明来给出一个直接证明。

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In the paper, we present a direct proof of Raney s intrinsic characterization of completely distributive lattices and give some applications of the intrinsic characterization.

本文对完全分配格的内蕴式刻划给出了一个简洁的直接证明，并给出了内蕴式刻划的若干应用。

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But it does not say there's proof of a direct connection.

CNN: Debate over fracking, quakes gets louder

While there is no direct proof of manipulation, there are a lot of sound reasons, based on flawed methodologies, and based on nearly every other underlying employment data series, not to trust the headline making unemployment data.

FORBES: Why Jack Welch Has A Point About Unemployment Numbers