Sentence examples for lines of proof from inspiring English sources
Its proof completely follows the lines of proof of Theorem 1 and hence it is 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.
The lines of proof are not effected and therefore the proofs are omitted.
From (ii), by following the same lines of proof as in Theorem 3.9, we get that (u in operatorname{Fix}(T)).
Moreover, following the lines of proof of the lemma in [4], we get ∫ Ω u 1 r d x < ∞ if and only if r > − 1. □.
With these lines of proofs, Algorithm AWCR generates a point sequence and every point of the point sequence consists of the K non-negative numbers, e.g., S 1 ( n ), …, S K ( n ).
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).
