Sentence examples for yields the proof from inspiring English sources
(2.5) This yields the proof.
This yields the proof of '⇒' in (2.12).
Combining the results of Corollary 1 and Lemma 3 yields the proof.
(2.10) This yields the proof of Case ((mathcal{B})) and Case ((mathcal{B'})).
Taking into account the last equality and (Z ( theta_{1};hat{u},x^{0} ) =E), (46) yields the proof of inequality (41).
Finally, choosing (lambda_=min{lambda_{0},lambda_{1},lambda_{2}} >0) we can deduce that max_{tgeq0}J tU < c^-C_{0}lambda^{frac{p}{p-q}} quadtext{for any } 0< lambda< lambda_, which yields the proof of this lemma.
If it can be assumed that the study should primarily yield the proof of efficacy for diclofenac 12.5 and 25 mg, and all other comparisons were defined as secondary endpoints, then the indicated statistical procedure of "Fisher's protected procedure" would be sufficient for the multiple confirmatory comparisons of diclofenac potassium 12.5 and 25 mg versus placebo.
These two propositions, as well as the four formulas yielded in the proof of Proposition 2, are very important for our batch sizing problem.
This yields, as in the proof of Lemma 2.4, that there exists x ∗ ( x ) ∈ X such that lim n → ∞ f n ( x ) = x ∗ ( x ).
Sidgwick's psychical research never yielded the hard proof of survival that he sought, and although at the end of his life he concluded that it had been largely a waste of time, he allowed that there were some positive results from it and that, at least in the 1890s, some promising new lines of research had emerged.
"In order to solve a case, the FBI must prove culpability beyond a reasonable doubt, and, unfortunately, none of the well-meaning tips or applications of new investigative technology have yielded the necessary proof," an FBI spokesperson told CBS.
