Sentence examples for a different proof from inspiring English sources

We gave a different proof.

However, we provide here a different proof.

For a different proof of (2.5), see [18] for details.

The case for all with a different proof is given.

We now give a different proof for it.

This will require a different proof, which issketched below.

In a different proof-of-concept clinical trial, autologous ADSCs were injected in patients with knee OA.

This is somewhat misleading, because, aside from implying an affinity to the Bitcoin blockchain (which uses a different, proof-of-work consensus algorithm), it also implies a considerable break with the past that hasn't really occurred, at least not on the technological level.

However, the fact that we are dealing with a system instead of a single equation forces us to develop a significantly different proof.

Here, we provide a slightly different proof.

Now we give a slightly different proof by Theorem 2.1.