Sentence examples similar to proved the proof of from inspiring English sources

"Now that we have proved the proof-of-concept, the road is clear to the first set of clinical trials just to see whether it'll work," he said.

Moreover we proposed a pattern for describing the Cloud resource and the Cloud application that is compatible with current emerging standards, as proved by the proof-of-concept editor for application and resource description, shortly described in this paper.

The necessity is proved and the proof of Theorem 3.2 is completed.

Equation (3.19) has already been proved (see the proof of (3.12)).

(16) is proved, and the proof of Theorem 4 is now completed.

Then, using the inductive method, the correctness of (26) is proved, and the proof of Theorem 3.1 is completed.

end{aligned} By the observation just after Definition 1 of (C_{NJ}^{(p)}(X)), we have (C_{NJ}^{(p)}(X geq1), so thesis (2) is proved and the proof of the theorem is completed.

As we have proved in the proof of Theorem 3.1, if this function has no constant sign on I then the Green's function must necessarily change sign in a neighborhood of (s=0).

We prove (i), the proof of (ii) is similar.

Proof We only prove (i); the proof of (ii) is similar.

Proof of Theorem 4.1 We only prove (i); the proof of (ii) is similar.