Sentence examples for step of proposition from inspiring English sources

Thus, as a next step of Proposition 1, we clearly get P E is p-Cockcroft (equivalently, efficient) for any prime p or 0. □.

As a next step of Proposition 3, the following result basically states that each semi-direct product presentation as in (2) which is obtained by condition (1) has a characteristic polynomial.

If (S_{X_{1},X_{2}}(x_{1},x_{2})) is non-degenerate bivariate survival function given by Eq. (12) and has differentiable marginal failure rates then it must satisfy conditions (18a) to (18c) in Theorem 4. Follows step by step the proof of Proposition 1 in Kulkarni (2006).

The next lemma is analogous to Step 2 in the proof of Proposition 2.7.

This follows since, otherwise, there is an element (g' in G {setminus }{1_G}) and a lift g of (g') in (Gamma ) such that a positive power (g^m) of g equals the neutral element (1_{Gamma }) (see Step I of the proof of Proposition 21).

Then, following the same steps as in the proof of Proposition 1 one gets the expressions for ( v_{c}(e_{c},e_{l})) and (v_{l}(e_{c},e_{l})).

One can reproduce the same steps as in the proof of Proposition 11 to conclude that if there exist small enough positive constants (zeta _{psi_{k_{2}}}) and (zeta_{lambda,ell}) for (1leellle D-1) and (lambdain I_{ell}) such that (53) holds, then equation (47) admits a unique solution in the space (H_{(beta,mu,k_{2},Omega )}).

Step 2. End of the proof of Proposition  3.2.

And lawyers for both sides had to spend some of their allotted time addressing the question of standing — whether the proponents of Proposition 8, who stepped in to defend it when California state officials declined to, had the right to do so in the first place.

The proof of this result follows analogous steps as those in the demonstration of Proposition 11, so we omit it.

The final step of the study was the proposition of remedial actions in order to improve the pedestrian mobility and walkability across the examined streets.