Sentence examples for the proof becomes from inspiring English sources

Therefore, the proof becomes straightforward as it was developed before.

Therefore, by using the Fejér monotonicity and the contractility, the rest of the convergence proof becomes standard.

It's hardly surprising, after a spell in which he lost his friend and D-12 colleague Proof, became addicted to prescription meds, went into rehab and considered suicide.

We prefer this approach, because the following proofs become more tractable.

In particular, construction of exponentially shorter proofs becomes possible.

In the appendix, we do not implement such three-parameter representation since the proof will become more cumbersome and prolix by employing the new one.

More than two state variables: With a number of state variables n, the square in the proof will become a hypercube in n dimensions, with 2 n corners, each corner representing a possible previous sequence of estimates of each of the n state variables.

We give a full complexity classification of all eleven 2-Π problems, observing that in the switch from one to two linear orders the complexity landscape changes quite abruptly and that hardness proofs become rather intricate.

This is the point where the proof in [24] becomes really complicate and requires some new ideas and deep arguments.

If you start your sales pitch with WHY the product exists in the first place, the product itself becomes proof of, as Sinek says, your "higher cause--proof of the WHY".

It is indeed a matter of time before the application of automated proof assistants becomes an everyday affair in the life of the mathematician; it is the grand challenge of the automated reasoning community to make it happen sooner than later.