Sentence examples for course of proof from inspiring English sources

In fact, in the course of proof of Theorem 3.1, Lemma 2.8 plays an important role.

For this reason, the course of proof in Lemmas 2.1 and 2.2 is not true.

In the course of proof it is shown that, the leading coefficient of the constituent polynomial q ( k ! l + r, k ) is k ! k - 2 ( k - 1 ) ! for every r = 0, 1, …, k ! - 1. Since each constituent polynomial is of degree k - 1, one can get the following estimate for q ( n, k ) : q ( n, k ) ∼ n k - 1 k ! ( k - 1 ) !. (2.7).

Assertions similar to the following lemma (see, e.g., [24]) were used (and proved) in the course of proofs of several fixed point results in various articles.

Of course, absence of proof notwithstanding, Giuliani was only amplifying a similar smear Trump made on the campaign trail.

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.

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

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.