Sentence examples for combine propositions from inspiring English sources

Next, we will combine Propositions 1 and 2 to see the complete dynamical picture.

In principle, one can combine Propositions 6.11 and 6.7 to obtain a bijective correspondence between special prefibrations over the simplicial replacement (Delta I) of a small category I and covariant lax functors F from I to ({text {Cat}}) in the sense of Definition 4.5.

However, it turns out that there is more: one can combine Proposition 3.8 and its dual into a single statement.

To see that if K ∈ W p, i n, there is equality in the inequality of the theorem, combine Proposition 2.6 with the definition of G p, i ( K ) to get ω n p / ( n − i ) G p, i ( K ) = inf { n ω n W ˜ − p, i ( Λ p, i K, Q ∗ ) W ˜ i ( Q ∗ ) p / ( n − i ) / W ˜ i ( Λ p, i K ) : Q ∈ K o n }.

For bodies with ith continuous curvature functions, the equality conditions for the inequality of Proposition 3.14 are easily obtained by combining Propositions 3.10 and 3.21.

Combining Propositions 1, 2, and 3, we have the following Proposition.

Now, combining Propositions 5.1 and 5.2, we get the proof of Theorem 1.3.

Combining Propositions 4.1 and 4.2, we get the proof of Theorem 1.2.

Combining Propositions 1 and 2 together, we can remark that the unique solution of (19) is (29).

Hence, combining Propositions 11.14 and 11.16, we can immediately formulate a generalisation of Theorem 11.6 as follows.

Combining Propositions 1.4 and Proposition 3.2 with Theorems 4.2 in [27] and Theorem 3.2 in [28], we immediately have the following theorem.