Sentence examples for the preceding proof from inspiring English sources

Similar to the preceding proof, we obtain that.

The proof of this statement is a total analogy with the preceding proof of Proposition 3.

Similar to the preceding proof, we obtain that lim i → ∞ x i = x ¯.

The preceding proof states that a bias does not affect the stability analysis.

Obviously, the choice of τ, the values of ϱ and ϵ in the preceding proof depends on λ.

For and, as the preceding proof in Theorem 2.1, there exist integers and mappings satisfying (2.5)–(2.7), where are replaced by, and,, respectively, and for some.

The proof of this statement is a total analogy with the preceding proofs as consequences of the main statements.

The proof of this statement is a total analogy with the preceding proofs of Corollaries 2 and 3. Thus we omit it.

The proof of this statement is a total analogy with the preceding proofs of Corollaries 2 and 3 (because Corollary 22 is a dual form of Corollary 6).

We recall from the preceding proofs that we can without loss of generality assume (Qle 0) and that we aim to bound the negative eigenvalues ({-lambda _i}) of (mathcal {H}).

Proof Using an idea in the proof of [2], Lemma 2, and the preceding theorem, the proof can be obtained easily, so it is omitted.