Question

みみ

2行目のprove to は人に証明するという使い方で良いのでしょうか？教えて頂きたいです。

14
Long experience has shown that practicing impromptu talks does
two things: it proves to the people who work at developing this skill
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that they can think on their feet, and this experience makes them
安
確心して
much more secure and confident when they are giving prepared talks/
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かくしん
自をもって
They realize that, if the worst should happen and they forget their
memorized material, they can still talk intelligently on an impromptu
basis until they remember what they were planning to say.

Answer 1

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ののののの

いいと思います。
ちなみに何を証明するかがその後ろのthat節です。

prove (to 人) that節
that節はproveの目的語です