Sentence examples for with this proof from inspiring English sources

Proof To start with this proof, a certain amount of linear algebra will be used.

With this proof, the useful model of Stone can be applied with confidence to a wide range of situations.

With this proof of principle, scientists hope versions of the AIDS virus engineered to carry different genes can now be applied to a variety of other diseases.

With this proof of concept, we demonstrated the feasibility of MTE using SPIONs for VFF cell guidance in 2D.

With this proof in hand, astronomers should be able to calculate the threats of these rogue bodies more precisely, although it's unlikely they'll be able harness the effect to save us from Armageddon.

With this proof of concept in hand, the researchers are trying to figure out how to scale up the practice to protect entire farms--and how to convince farmers to adopt it.

With this proof-of-concept, the value of developing tissue-engineered PDL around dental implants was highlighted.

In keeping with this proof-of-concept study design, we also restricted our choice of hyperemic stimuli to those most commonly employed for in vivo assessment of the microcirculation, namely, adenosine and papaverine.

Compare this proof with the proof of Proposition 2.1 in [19].

Compare this proof with the proof of Theorem 2.7 in [18].

Compare this proof with the proofs of Proposition 8 in [15] and Proposition 9 in [5].