Sentence examples for proved in setting from inspiring English sources

The fixed point results are proved in setting of such spaces and some examples are given to verify the effectiveness of the main results.

In fact, essentially all mathematical facts whatsoever can be stated formally and proved in set theory.

All mathematical facts about these notions can then be proved in set theory.

One also defines versions of the natural numbers by: 0 = ∅, 1 =, etc. Again, all facts about numbers and functions on them can be proved in set theory.

Similar extensions of the results as found in [21 23] may be proved in our setting.

We have given also some examples to support the results proved in our setting.

His first and most successful patents concerning flour-milling proved the most problematic to defend, and Evans' battles proved influential in setting precedent for the newly established area of federal patent law.

The cost of restoring order and building up integrated political institutions at all levels throughout the country proved important in setting China's course for the next two decades.

Goodwillie's headed flick-on proved crucial in setting up Rooney to unleash a dipping half-volley from 25-yards that, despite his best efforts, Mannus failed to prevent finding the top right corner.

Incidental music and sound effects were provided by Desmond Briscoe of the BBC Radiophonic Workshop and these proved significant in setting the mood of the play – sections were later used in a BBC educational programme on the effectiveness of incidental music.

But along with the battle to control state legislatures, they could prove significant in setting the nation's political landscape for the next decade.