Sentence examples for in the same proof from inspiring English sources

I tasted two bourbons, side by side, that had been distilled with the same recipe, put in the same proof and at the same time, and stored in similar warehouse locations.

Remark 3.1 We have noticed in the proof of Theorem 3.1 that B 1 ≈ A ¯, where A ¯ is defined in the same proof.

The fact that the classical rules go beyond the intuitionistic rules and yet the latter already suffice for unique characterization means that there is no 'live and let live' option available for the intuitionist, of recognising that the intelligibility of two distinct negation connectives, classical and intuitionistic, which can cohabit in the same proof system each with their respect rules.

On the prooV platform, enterprises can test, evaluate and compare several technology solutions in the same proof-of-concept, rather than running a different proof-of-concept for each technology and having to compare the results afterward.

From (i) in Theorem 2.2, using the same proof procedure as in Corollary 2.4, we can obtain the corresponding conclusion.

By Lemma 3.1 and the same proof in Lemma 3.2, we have the following lemma.

There is no essential dificulties to apply the same proof in our case.

It is the same proof as in [9], Lemma 3.1.

Then, by the same proof as in the first part of Lemma 2.2, one gets.

In fact, the same proofs, based on Lemma 9, can be followed through point by point.

In theory, proof-of-stake does not offer rewards in the same way proof of work does, only transaction fees.