Sentence examples for auxiliary statements from inspiring English sources

Before continuing, we give some auxiliary statements.

Moreover, in this section we give some auxiliary statements.

In Section 2 some auxiliary statements and in Section 3 main statements are given.

In this section, auxiliary statements necessary for the subsequent analysis are formulated.

Here we give the following auxiliary statements which are introduced in [27].

In Section 5.1 we present several auxiliary statements about the limits of the martingales.

In the sequel, we will need the following auxiliary statement.

Let us cite the following auxiliary statement from [3].

Here these results are formulated into an auxiliary statement in the form of Lemma 1, and they will be further used to solve the problem (1), (2).

Strong verification required that the truth of a proposition be conclusively ascertainable; weak verification required only that an observation statement be deducible from the proposition together with other, auxiliary, propositions, provided that the observation statement was not deducible from these auxiliaries alone.

The abrupt descent into particularity in every statement of this kind – Being itself made an auxiliary to some momentary accident of being – may only startle in the dark of night, when the intuition comes that there is no proportion between the great given of existence and the narrow vessel of circumstance into which it is inevitably forced.