Sentence examples for proof by using from inspiring English sources

They accomplish this proof by using a ray fired into a specific scene to simulate the universal Turing machine.

Second, we prove that the up down equilibrium point is a saddle via an elementary proof by using the Routh–Hurwitz criterion to show that the Jacobian matrix valued at the point has two and two eigenvalues in the open left- and right-half planes, respectively.

Proof By using (13), we get.

Proof By using (30) and, we get the theorem.

Here we plan to finish the proof by using contradiction.

This completes the proof by using Lemma 2.3.

Finally, the proof of (iii) follows by using similar arguments as in the proof of (iii), Theorem 2.1.

Then ⪯ η is a partial order on X. Proof The proof follows by using the cone metric axioms, properties (2) and (3) for the cone, and (3.1).

The proof follows by using the convexity of Orlicz functions.

Another way of completing the proof is by using (3) of Lemma 2.

(iii) The proof follows by using the convexity of Orlicz functions.