Proofs are presented with a "proof idea" component to reveal the concepts underpinning the formalism.

证明是通过“明思想”出的，深刻揭示了支撑形式层面的本质概念。

youdao

So that's basically the idea of a proof.

这就是证明的思想了。

youdao

So, that's the end of the proof. OK, so you see, the idea is really the same as for Green's theorem.

这就是最终的证明了，证明的思路和证明格林定理的是一样的。

youdao

Professor Yoshino explains. "Shakespeare calls this a problem of ocular proof, the idea that we need to see evidence before we believe in it -- and that,oftentimes, when metaphysical questions of guilt or innocence are difficult for us to answer, we have a tendency to reduce them to questions that pertain to physical evidence.

VOA: special.2011.06.06

Social proof and the idea of a nation as an imagined community.

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Essentially, the bill would move to the front of the visa line any immigrant with a business idea and proof of investor interest.

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The arsenic-eating bacterium, written up in the current issue of Science, provides a muted proof of concept for this idea.

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