Sentence examples for presented in the proof of from inspiring English sources

Letting in the estimation of, presented in the proof of Theorem 2.12, we get (2.34).

The proof follows closely the ideas presented in the proof of Theorem 4.1.

Theorem 2.2 can be proven by using the ideas presented in the proof of [28], Theorem 3.3.

By using the same arguments presented in the proof of Theorem 2, the desired result follows directly from Proposition 3. □.

The key technique to prove this theorem is already presented in the proof of Theorem 2.2, so we here only highlight some parts which need to be modified.

there exist such that for all and, there exists such that (2) Letting in the estimation of, presented in the proof of Theorem 2.12, we get (2.34)  .

The corresponding decay estimates to the solutions will be presented in the proofs of the theorems for brief expressions instead of in the statements.

The key technique to prove this corollary is already presented in the proofs of Theorems 2.2 and 3.2, so we here only highlight some parts which need to be modified.

With another -sharp" embedding theorem, the complete analogue of Theorem 4.3 is true also when we replace the left side by The proof needs small modification of arguments we present in the proof of Theorem 4.3.

Although the substance is presented in the whole proof of [4], Theorem], we should restate and prove it in our context for the readers' convenience.

It does not yet use the framework to perform the language processing present in the proof-of-concept.