Sentence examples for first lemma supporting from inspiring English sources

In the first lemma supporting Theorem 3.4, we show that the requirement that and be nonmonotone can essentially be lifted.

Firstly, we give the following lemma supporting our main conclusion.

The first Lemma establishes that the loop invariants hold.

The first lemma is the well-known Kiguradze's lemma.

The first lemma is taken from [8].

The first lemma is easy to prove.

In the first lemma we consider the expected number of external loops.

In the first lemma we look at the number of external loops.

Our first lemma characterizes the compactness in terms of sequential convergence.

The first lemma states the existence of a quasi-optimal refinement T ^ of T ℓ under certain assumptions guaranteed by Lemma 3.5 in case that the estimator satisfies the axioms stability (A1), reduction (A2), and discrete reliability (A4).

Third is supporting basic research.