Sentence examples for proves case from inspiring English sources

This proves case (i).

On the other hand, from p + q ≥ 0, that is, p ≥ − q, it is acquired that S ˜ ( p, q, t ) ≤ S ˜ ( − q, q, t ) = 1, which proves Case 2 and the sufficiency is complete.

Noticing that p + q ≥ 0, that is, p ≥ − q, we have T ˜ ( p, q, t ) ≥ T ˜ ( − q, q, t ) = 1, which proves Case 2 and the proof is finished.

At the same time, since p + q ≥ 0, that is, p ≥ − q, we have C ˜ ( p, q, t ) ≤ C ˜ ( − q, q, t ) = 1, which proves Case 2 and the sufficiency is complete.

It is not yet a proven case.

Next, we prove case (ii).

Now, we prove case (ii).

We prove case (ii) and case (iii).

Since it is easy to prove Cases (ii) and (iii), we only prove Case (i).

Thus, we prove case (ii) in Lemma 8.1.

In a similar way to proving cases 1 and 2, we can prove case 3. Finally, we will prove (rho_{2}(f)=rho_{2}(g)). Suppose that (rho (f)=infty).