Sentence examples for those proofs from inspiring English sources

So, the techniques in those proofs are not applicable in the unbounded case.

Recall that the procedures has become more and more complicated in those proofs.

This theorem is proved by arguments analogous to those proofs of Lemma 4.2 and Theorem 4.3.

But those proofs, although extremely complicated, were based on techniques that were broadly familiar to experts in the field.

Creating ways for multi-party transactions to engage in queries that prove certain facts about a business, without ever accessing the data underlying those proofs.

But each time, upon diverting his attention from the premises, he finds himself back at the bottom of the hill, wondering about the credibility of those proofs that seemed so evident: "perhaps some God could have given me a nature such that I was deceived even in matters which seemed most evident" (Med. 3, AT 7 36).

Having customers there, it's nice to have those proof points".

The definition of validity singles out those proof structures which are 'real' proofs on the basis of the given reduction procedures.

He says the purpose of his department is to create those proof points and to break down functional silos by working across departments to improve the sales cycle and give customers different ways to interact with the company.

(Superb examples of those two proofs are on view).

If as a philosopher he should happen take up the question of the immortality of the soul, he is going to regard with suspicion those classical proofs which rely on an analysis of thinking as a non-physical process.