Sentence examples for corollary by from inspiring English sources

To which we have a corollary: by proverbs we enliven copy.

We have the following corollary by Theorem 1.1.

For (20), we have the following corollary by Theorem 2.1.

We can easily deduce the following corollary by utilizing the same technique as in Theorem 3.4.

Similar to Corollaries 1 and 2, there is also a corresponding corollary by Theorem 7 here.

Then, it is straightforward to obtain the following corollary by letting N 0→0.

From Theorem 4.1, we immediately obtain the following corollaries by (33) and (38).

As examples, in Theorem 1.1, we can obtain some corollaries by choosing different and as follows.

From Theorem 3.1, we immediately obtain the following corollaries by the formulas (20) and (30).

We obtain the following two corollaries by making use the above operator and, respectively, letting α → β and → ( 0, 0,).

In a fashion similar to the proofs of Corollaries 2.3 and 2.4, we can prove the following corollaries by using Theorem 2.2 instead of Theorem 2.1.