Sentence examples for needed for proof of from inspiring English sources

The report says the abuses clearly meet the threshold needed for proof of crimes against humanity in international law.

On request, we will provide you with a certificate of participation, which might be needed for proof of attendance for your employer.

With all that information in hand, Arman helped figure out what experiments were needed both for proof of concept and for grant applications.

We give some definitions and observations needed for the proof of claim (1) of Theorem 6. Fix any admissible ((n,theta )) and (mu in (-infty,, mu ^n(theta,a,b))).

So, in the following we give some well-known results, which are needed for our proof, of the classical Nevanlinna theory without presenting proofs.

These state that disruption and reconstruction of the gene under investigation coupled with loss and regain of the phenotype is needed for firm proof of a functional role.

In this section, we introduce some notations and definitions of fractional calculus [1, 2] and present a lemma needed for the proof of our main results.

Section 2 is devoted to the definition of the Sobolev-Lorentz space, as well as several lemmas needed for the proof of Theorem 1.1.

Only the former is needed for the proof of Frege's Theorem, however.

In Section 2, we introduce some lemmas needed for the proof of our main results.

The following lemma will be needed for the proof of our main result.