Sentence examples for for its proof from inspiring English sources

By an example, however, we show that their result is not correct and so we give the correct form of it applying a new method for its proof, by establishing a separation theorem.

Accenture admits that most UK stadiums lack a powerful enough WiFi system to support a truly connected experience; the firm had to build a new network at Twickenham for its proof of concept.

Some absurdly gifted footballers will be on show in the quarter-finals that start tonight, but the tournament may be enthralling for its proof that the risk of embarrassment and failure cannot always be kept at bay.

It was hardly an occasion for merely appreciating the side that had denied City a win, but this game ought to be valued for its proof that diversity remains in a competition that is supposed to embody the highest standards of football on our continent.

For its proof see [14], Proposition 3.

For its proof, see Remark 15.

At the turn of the 19th Century, David Hilbert (1862 1943) presented, in his Grundlagen der Geometrie, Euclidean geometry as an axiomatic subject that did not depend on diagrams for its proofs (Hilbert 1899).

There are several versions of its proof; see, for example, [2, 7 9].

But it is perfectly meaningful; people have been wondering whether it was true or false for centuries; and its proof by Andrew Wiles has been a substantial discovery.

For our introduced problem (our particular equation), it is noted that the (H_{0}^{1} ( Omega ) )-norm remained true for (2.11), and its proof is very similar to that in [2].

The following lemma was proved in Section 3 of [4] but for convenience of the reader, we have reproduced and included its proof for ready reference.