Sentence examples for course of a proof from inspiring English sources

A natural deduction proof is a sequence of wffs beginning with one or more wffs as hypotheses; fresh hypotheses may also be added at any point in the course of a proof.

Inability to see any such necessity is, of course, not a proof that such a necessity does not obtain.

In the course of the proof, an infinite dimensional analogue of the Weierstrass approximation theorem is also established onE*.

In the course of the proofs, a representation of the Lévy process as a function on K′ is obtained and stochastic Lévy integrals are studied.

for.The case In the course of the proof of Theorem 1.2, we have established (2.25) (2.25).

The course of this proof as regards the techniques heavily relies on Holm [10].

where and are positive constants to be fixed in the course of the proof.

In order to prove the above theorem Theorem 3.3, we divide the course of the proof in three steps.

In the course of the proof, it is also shown that the space (Jp) is isometrically isomorphic to the Bargmann-Segal analytic functions on bJ−p under S-transform.

In [8], Huang and Jia applied the basic Lemma 2.3 and the famous Zorn lemma to show the existence of minimal members in the course of the proof of their other main theorem (Theorem 3.1) (see line 33 of p.48).

Established with just 50 free online courses as a proof-of-concept, MIT's groundbreaking Open CourseWare project quickly expanded to 1,700 courses through a worldwide consortium of universities in just three years [PDF].