Sentence examples for asserted by the following from inspiring English sources

Setting (mathtt{k}=1) in Lemma 2, we obtain an identity asserted by the following corollary.

Setting (mathtt{k}=1) in Theorem 2, we get a little simpler inequalities asserted by the following corollary.

Applying Eq. (3.10) to Eqs. (2.7), (2.8) and (2.27), we get some interesting identities asserted by the following corollary.

Applying (2.7) and (2.11) to (2.9) and considering (2.8), we obtain two interesting identities asserted by the following theorem.

Here we give the answers for k = 2 and k = 3 in (2.10) asserted by the following lemma.

We begin by presenting an integral formula involving the functions (31) and (32), which is asserted by the following lemma.

A financial institution that has fully complied with the error resolution requirements has no further responsibilities under this section should the consumer later reassert the same error, except in the case of an error asserted by the consumer following receipt of information provided under paragraph (a)(1)(vii) of this section.

The Prosecution asserted that the following considerations supported its motion for joinder.

To do this, we first observe a simple property asserted in the following lemma.

Our eleven main identities are given here in the form of a single unified result asserted in the following theorem.

The following corollary states that (psi(T)) is with high probability much smaller than (varepsilon^{-3kappa}) as asserted by the Definition 11 for (Tleqtau^{ast}).