Sentence examples for the the proof of from inspiring English sources

The the proof of the theorem doesn't depend on the supposition that likelihoods are objective or have intersubjectively agreed values.

As in the the proof of Theorem 3.3, T = { T ( t ) : 0 ≤ t < ∞ } is a semigroup of nonexpansive self-mappings on D. It follows from Lemma 2.1 that {y n } is an approximating fixed point sequence of semigroup.

In fact, according to John Bell (Mermin 1993, p. 805), von Neumann's assumptions (about the relationships among the values of quantum observables that must be satisfied in a hidden-variables theory) are so unreasonable that the "the proof of von Neumann is not merely false but foolish!" Nonetheless, some physicists continue to rely on von Neumann's proof.

These data support the findings of the proof-of-concept study.

These results support the findings of the proof-of-concept study.

On the basis of the proof-of-concept study we identified two important challenges.

The proof of the pecking order?

The proof of the proof's identity is finally, as the mathematicians say, fairly trivial.

The proof of the superiority of the rich?

But the proof of the pudding is in the eating.

"But the proof of the pudding is in the tasting".