How do you use proof in a sentence?

I believe that he stole my purse, but I have no real proof.

The district attorney offered proof that she stole millions from her employer.

To me, a newborn baby and the wonders of nature are proofof God's existence.

What proof does the researcher have to validate his hypothesis?

The stockpile of the victim's jewelry found in his home is proof that he's the killer.

Are hives proof that she's allergic to strawberries?