Sentence examples for be useful for proving from inspiring English sources

We present a short proof of a slightly stronger result which might also turn out to be useful for proving the VPN Tree Routing Conjecture for general networks.

The following lemma will be useful for proving our results.

The same methods should also be useful for proving the statement for (n=5,6).

The following lemmas will be useful for proving the convergence result of this paper.

It also extends the latter to include the complex eigenvalues case and will be useful for proving Theorems 9 and 10.

As the machine learner is trained on previous proofs, it recommends relevant premises from the large library that (according to the past experience) should be useful for proving new conjectures".

To begin with, we prepare some lemmas which are useful for proving oscillation criteria, Theorem 1.1.

It is known that differential inequalities are useful for proving the existence of extremal solutions of ODEs and hybrid differential equations defined on J.

These results are useful for proving the solutions of nonlinear functional differential and integral equations which may depend upon the past history, present data and future consideration.

Fixed point theory constitutes an important and the core part of the subject of nonlinear functional analysis and is useful for proving the existence theorems for nonlinear differential and integral equations.

It is known that differential inequalities are useful for proving the existence of extremal solutions of the ODEs and hybrid differential equations defined on J. the function (t mapstofrac{x}{f t,x }) is continuous for each (x inmathbb{R} ), and.