Sentence examples for required hypotheses from inspiring English sources

Thus, all the required hypotheses of Corollary 2.7 are satisfied.

Now, all the required hypotheses of Theorem 2.2 are satisfied.

Then all the required hypotheses of Theorem 2.4 are satisfied.

It is easy to see that X satisfies all the required hypotheses in Corollary 3.

Thus f and X satisfy all the required hypotheses in Corollary 4.

From the above arguments, we conclude that (2.13) holds; hence, all the required hypotheses of Theorem 2.3 are satisfied.

Scientific progress requires hypotheses and ideas, but it is enabled by resources.

So testing Whorfian hypotheses requires testing two independent hypotheses with the appropriate kinds of data.

These hypotheses required enroling 460 patients.

Examining these different hypotheses required different approaches.

Testing the spring sources would be expensive and, Dr. Matte said, would require some hypothesis about what the research was looking for.