Sentence examples for in its proof from inspiring English sources

In fact, in its proof, it is not essential that F is continuously differentiable in t.

As in its proof, it follows from (i) and (ii) that Assumptions (i) and (ii) of Theorem 2.6 are satisfied.

In its proof, the notion of weak containment for C⁎-correspondences plays an important role.

"When I read the book in its proof form, I called up Alex Ross right away," said Jude Kelly, the artistic director of the Southbank Centre, speaking to journalists and music professionals at the press launch.

Nevertheless, additional mistakes can be found in its proof.

Most of the ideas in its proof go back to Baillon's work [8].

Algebra and an understanding of discrete probability will take the reader through all but the appendix, which utilizes probability measures in its proofs.

Moreover, the strong convergence of this algorithm can be proved by an argument similar to the proof of Theorem 3.4 (in fact, its proof is much simpler than that of Theorem 3.4).

These places are far from counter-example to the supposed spread of freedom; they are in fact its proof.

The criteria for a theory T's "recognizing" its consistency statement as such are met just in case it can be proved in T that its proof predicate satisfies the three Hilbert-Bernays derivability conditions as given in Hilbert and Bernays 1934.

The following Bogovskii lemma will be needed in Lemma 4.3; its proof can be found in [24].