Sentence examples for by using the proof from inspiring English sources

This lemma can be proved easily by using the proof technique in Lemma 2.1.

By using the proof of Theorem 3.2 and Remark 3.5, we know the following: if with and (3.20).

By using the proof of Theorem 3.5, there exists a unique multi-(C^ -ternary algebra homomorphism (H : A rightarrow B) satisfying (20).

Proof By using the proof of Corollary 2.5, there exists a unique C ∗ -ternary algebra homomorphism H : A → B satisfying (2.9).

Next we give the weak convergence of Picard iteration in a uniformly convex Banach space by using the proof technique developed in Reich [19, 32].

By using the proof of Theorem 3.2, there exists a unique (C^ -ternary algebra homomorphism (H : A rightarrow B) satisfying (5).

4 AM-NutzenV] and is differentiated by using the categories proof, indication, hint, no proof and no indication (Section 3.1.1 IQWiG GM 4.0).

By using the same proof as Theorem 3.2, we can easily obtain the following conclusions.

By using the same proof of Theorem 1, we show the existence of optimal controls.

By using the same proof, we obtain that and are nonexpansive.

In addition, the stability of the pinning-based consensus algorithm defined in (4) also can be ensured by using the same proof.