Sentence examples for preceding lemma from inspiring English sources

Let, be as the preceding lemma.

Let and be as the preceding lemma.

The constraint (4) follows immediately from the preceding lemma.

From the preceding lemma, we can also deduce the following.

By the preceding lemma, we directly obtain the following lemma.

It follows from the preceding lemma that S is orbitally continuous.

Analyzing the constructions of the preceding lemmas, the following observations can be derived.

With the help of the preceding two lemmas, we can now prove the existence of solutions of BVP (1.1 - 1.2 1.1 - 1.2

In connection with the preceding facts, based on Lemma 1 and Theorem 1, we are now in a position to formulate the following new statements as direct consequences of the Axiom of Infinite Choice.

Proof Using an idea in the proof of [2], Lemma 2, and the preceding theorem, the proof can be obtained easily, so it is omitted.

From the preceding discussion (above the proof of this lemma), φ uniquely extends to a positive map on (mathcal{A}+Jmathcal{A}).