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

This is a useful lemma that we will use in the proof of the main result.

In this section, we give some results which we shall use in the proof of theorems.

We present here the matrix inequalities that we will use in the proof of our main results.

Employing the technique that we use in the proof of Theorem 3.1, we get ∥ v n − s ∥ ≤ ∥ u n − s ∥.

The following result obtained by Clarke in [28] is the main idea which we use in the proof of Theorem 16.

The coding scheme that we will actually use in the proof of Theorem 7 is more complicated, and we will refer to it as subtle coding.

Therefore in this section, we describe our graph-based relational memory, the relations between nodes and the overall memory architecture used in the proof-of-concept system.

Afterward, we briefly discuss important processing parts, called visual routines, that are used in the proof-of-concept implementation of the described architecture.

In this section, we collect some useful results that will be used in the proof of the theorem.

Firstly, let us prove a conclusion which will be used in the proof of Theorem 3.2.

Let us begin with some lemmas, which will be used in the proof of Theorem 1.1.