Sentence examples for for the complete proof from inspiring English sources

For the complete proof see [49].

We refer the reader to Section 8.1 for the complete proof.

By duality, we find the optimal pairing P* when all of the following conditions hold true (for the complete proof the optimality of this algorithm, the reader is referred to [25]) the following: (a).

[Here, we accept the proposition and other presented propositions without proof. For considering the complete proof and further reading of these propositions, please refer to Azevedo and Paxson (2010, 2014) and Nishihara (2011)].

For the complete proofs of the result, we refer the reader to [24].

For the complete proofs of these theorems, we refer to (Selvitella 2017), while for a brief sketch of the proof of Theorem 1 in the stationary case, we refer to the upcoming Section 5. □.

In particular, our result contains a 2H rmax -approximation algorithm for ECP, which gives an independent and complete proof for the result first obtained by Jain et al. (Proceedings of the SODA, 1999, p. 484–489).

For a sound and complete proof system for logic with an empty domain, see (Tennant 1990).

Here we give a complete proof for the reader's convenience.

Priest (1992) gives a sound and complete proof theory for the given semantics, but this is left for the reader to consult.

For complete proofs, see [415] or [497, Theorem XIII.31].