Sentence examples for result was proved from inspiring English sources

This result was proved by Kusuoka in a different form.

In [10] the following result was proved.

In [8, Theorem 1], the following existence result was proved.

The following result was proved by Aoyama et al. [6].

This result was proved independently by Nemytskii [10].

The following result was proved by Xu [14].

This important result is proved mathematically.

This result is proved by using the implicit function theorem.

The same result is proved for elliptic manifolds.

Thus, our result is proved.

Hence the result is proved.