Sentence examples for proof can be derived from inspiring English sources

In addition, the proof can be derived from Christoph and Schreiber (1998, formula (9)).

The proof can be derived along the similar lines to those in ([37], Theorem 9.1), which is omitted here.

Then, there are L square rank one matrices given as A1, A2,..., A L, such that A = A1 + A2 +... + A L and an alternative proof can be derived for such matrices.

No proof can be derived from our study; however, our findings support the public opinion collected from focus group discussions and recent ethnographic research that Bangladeshi police extort money from the population [ 5, 26, 40].

Alternatively, these proofs can be derived, assuming (tilde{u}^+ = -tilde{u}) and (tilde{v}^+=-tilde{v}).

From both investigations, no proof of efficacy can be derived for the coenzyme Q10 for migraine prophylaxis due to methodological reasons.

Finally, because of the observational nature of the study, no proof of causation can be derived from the abovementioned associations between glycaemic control and ICU mortality.

We omit the details of the proofs since they can be derived from similar ideas used in Section 3. We state our main results in the first subsection and we give a concrete example in the second subsection.

On Wittgenstein's view, we invent mathematical calculi and we expand mathematics by calculation and proof, and though we learn from a proof that a theorem can be derived from axioms by means of certain rules in a particular way, it is not the case that this proof-path pre-exists our construction of it.

The proof of Theorem 1.2 can be derived from Lemma 2.2 and Lemma 2.3.

Proof All the assertions can be derived from [[13], Chapter XV]) as it has been noticed earlier.