Sentence examples for by using three lemmas from inspiring English sources

In Section 3, by using three lemmas, the unique solvability of the difference solution is discussed.

He then solved the CLP case (a circle, a line and a point) using three lemmas.

We use two lemmas.

Then we discuss the stability of the semi-trivial periodic solution in two ways by using Lemma 1 and Lemma 4, respectively.

Then we can get the following two lemmas by using Lemma 3.1.

By using the two previous lemmas, we get the following.

To prove that under the hypotheses of Theorem 1.1, the relations (2.2) and (2.8 - 2.10) hold true, we show them by using the following four lemmas.

And we will show a theorem that an upper bound for Ψ ( 1 1 − θ v ) is expressed with Ψ ( v ) by using the following two lemmas.

We will use three times the Opial's Lemma 2.1.

In the final step the theorem is proved by using the Lemma.

By using Lemma 2.2, we can prove the following lemma.