Sentence examples for proof results from inspiring English sources

If t-norm T is of H-type and f: S → S is a strong (b n )-contraction, then there exists a unique fixed point x ∈ S of the mapping f and x = lim n → ∞ f n p for every p∈ S. Proof: The proof results from the Proposition 1 directly.

A result is presented together with its proof (Result 1), and the model of weighted goal programming with logarithmic deviational variables is then presented.

A "moderate," "weak," or "very weak" level of proof resulted in a "conditional" recommendation ("should probably be done", "should probably not be done…").

These aren't methods that generate fool-proof results, of course, and there's a lot that can't be seen reliably with the naked eye.

In particular, our approach reduces the complexity of the required proofs, resulting in fewer proof obligations that need to be discharged at the target machine.

Using similar arguments as in the proof of result (iii), result (iv) can be proved.

Proof The results follow immediately from the corresponding results for Steiner trees, see e.g., [41].

And women want solid proof of results.

The bridge configuration, a finite element model developed for design and the proof test results are described in this paper.

Proof The results of (i - ii) follow from Defi - iin 3.3.

For the proof of results, we give the following assumptions.