Sentence examples for useful to prove from inspiring English sources

It is also very useful to prove the above proposition.

The following results are useful to prove our main result.

The following proposition is useful to prove the exponential convexity.

The following definitions will be useful to prove the main results.

The following lemmas will be useful to prove our main results.

The contractivity condition can also be useful to prove some properties of the binary relation.

The following lemmas are useful for us to prove the main result.

The results of Theorems 1, 2 and 3 provide a useful method to prove the inequalities for triangles.

The beta-convergence approach proves useful to examine regional variations in population aging across Europe.

The following lemmata are useful in order to prove Theorem 4.1.

In the sequel, we need the following useful known lemmas to prove our main results.