Sentence examples for gave the proof from inspiring English sources

Later, Das and Vatsala [4] gave the proof and extended the result by constructing the Green function.

In [33] Yoshida and Miyamoto considered the case when q = 0, m = 0 and a = 0 about Theorem 1.10 and gave the proof.

Mascioni [5], in 2002, gave the proof for and gave the counter example to show that the above result is not true for.

First, Proclus does not ascribe a proof of the theorem to Pythagoras but rather goes on to contrast Pythagoras as one of those "knowing the truth of the theorem" with Euclid who not only gave the proof found in Elements I.47 but also a more general proof in VI. 31.

This gives the proof.

This gives the proof of the statement.

The gives the proof of Theorem 3.2.

This gives the proof of the theorem.

Then we give the proof as before.

For completeness, we give the proof.

We give the proof of Theorem 1.2.