On the other hand, "Proving and improving" shows a lot of hits in Google Books: https://www.google.com/search?udm=36&q=%22proving+and+improv...

It's possible that you both hit upon or recalled the same cool phrase, especially if the "proving" part was pre-decided and you were thinking of making an incremental improvement.

True, I agree but but its eerie they were written 2 days apart. Resting my case, thanks