Sentence examples for proof has been completed from inspiring English sources

Therefore, the proof has been completed.

We can argue as the proof of Lemma 2.6, so the proof has been completed.

It is obvious that z ± ≠ 0. The proof has been completed.

Especially for t = 0, it follows that | ϕ ( 0, ω ; t 0, ϕ 0 ) | 1 2 ≤ ρ 2 , ∀ t 0 < t 2. Thus, the <span class="lh">proof has been completed.

The proof of the theorem has been completed.

Therefore, the proof of Theorem 3.4 has been completed.

The proof of Theorem 2.3 has been completed.

The proof of inequality (2.24) has been completed.

The proof of Proposition 2.7 has been completed.

In summary, we conclude that the proof of Theorem 1.2 has been completed.

Combining (3.7) and (3.8) gives ∥ D ( G ( u ) ) ∥ ⋆, M ≤ C 3 ∥ u ∥ s, M. The proof of Theorem 3.3 has been completed.