Sentence examples for both cases we prove from inspiring English sources

In both cases, we prove that our assumptions are optimal.

In both cases, we prove that formally second-order time-accurate ALE schemes can be designed.

In all cases, we proved that is bounded.

For both cases, under suitable conditions we prove the existence and uniqueness of solutions to SRFDEs by using a contraction principle and the method of successive approximations.

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

Next, we prove case (ii).

Now, we prove case (ii).

We prove by cases.

We prove only case (i).

We prove this case in two steps.

Now, we prove the case (b).