Sentence examples for proof is concluded from inspiring English sources

Therefore, the proof is concluded.

and the proof is concluded.

Then G = constant in (0, +∞) and the proof is concluded.

The proof is concluded by applying Lemma 2. Proof.

As a consequence condition (iv) is satisfied and the proof is concluded.

In either case we get a contradiction to the maximality of (N_0) and the proof is concluded.

By using (64), the proof of (21) is concluded.

The latter equation of (19) is obtained by setting κ 2 ≜ A 2 η 2 − s 2, and the proof of (19) is concluded.

end{aligned} Hence, the proof of the theorem is concluded.

Hence, using (A.2), the proof of Lemma 2.4 iii) is concluded.

After these preparations, the proof can be concluded quickly.