Sentence examples for line of proof from inspiring English sources

By a similar line of proof to ψ ∈ D ∗, we can obtain ϕ ∈ C ∗.

We use the line of proof of Theorem 3.1 in Ng et al. [9] to prove this result.

Following the line of proof of lemma 3.1 we immediately obtain qk exists for any q ∈ F and, ∀i ∈ {1,2,... N}.

With the help of the line of proof in [21] that did not consider an intruder, for a network with an intruder, the average CEP can be written as (62).

Following the same line of proof, it can be easily seen that the same results hold true if the starting coefficient (alpha_{0}=max{ frac{1}{2},h(x_{0})}) is substituted by (alpha_{0}=max{b,h(x_{0})}), where (bin 0,1)) is a fixed and arbitrary value.

As shown in the following steps, we can focus ourselves on the main line of proofs and employ some automated reasoning package to deal with the less important branches.

Its proof completely follows the lines of proof of Theorem 1 and hence it is omitted.

The lines of proof are not effected and therefore the proofs are omitted.

Hence similar to the lines of proof of Theorems 5 and 7 our result follows.

Follows the lines of proof of Theorem 3.9 [8], so is omitted.

Following the lines of proof of Theorem 2.1, we get that problem (1.1) has a solution in W 0 1, p.