Sentence examples for in the first assertion from inspiring English sources

Note also that we have verified that ( L ˜, C × A ) ⊆ ˜ L ( R ˜ 1, C × B ) in the first assertion.

In order to prove the first assertion we only need to verify that A is nonnegative under the conditions (3.2), (3.4), (3.5), and (3.6).

In order to prove the first assertion we only need to verify the nonnegativity of A when (3.1) and (3.3) hold.

In order to prove the first assertion it suffices to show that Re ( 〈 ∂ ρ ( w ), w − z 〉 ) − ρ ( w ) > 0 for any w ∈ D ¯, z ∈ D. (9.12)Indeed, one first observes that if D is strictly convex and sufficiently smooth then Re 〈 ∂ ρ ( w ), w − z 〉 > 0 for any w ∈ D ¯ ∖ { z } (see [20] for the proof of this fact) so that Re 〈 ∂ ρ ( w ), w − z 〉 is non-negative in D ¯ and it vanishes only at w = z.

This was the first assertion in Australia of criminal misconduct against the global media giant, which has been dogged by allegations of illegal phone hacking at its British tabloids.

Hence, begin{aligned} sigma _n(h,P,x =sum _{|k|the first assertion in part (c).

Since ψ φ ‴ + 3 ψ ″ φ ′ + 3 ψ ′ φ ″ ∈ A β, 0, it follows from (20) that the sequence ( z n ) n ∈ N has a subsequence ( z n k ) k ∈ N with φ ( z n k ) → ∂ D. Therefore, applying ( z n k ) k ∈ N to the first assertion in (ii), we arrive at a contradiction to (20), finishing the proof.

The equality D s M G = L G ∩ H follows immediately from Lemma 10 and the first assertion in the statement of this theorem.

Proof The first assertion is an immediate consequence of Lemma 4 in [31].

First, doesn't the first assertion deny our colorblindness?

Thus, the first assertion.