How to (actually) prove it – New Frontiers of Mathematics and Computing in Lean

The magic ingredient here is this weird little tool for planning Lean projects called Lean Blueprints. Blueprints are a mechanism mathematicians have designed for planning out formalisations of their results. When translating a pen and paper result into a proof assistant, a mathematician must first encode all the necessary definitions, helper lemmas and so on before they can write the proof. The blueprint serves as a mechanism to keep track of this process. The above image shows an example blueprint, taken from Terrence Tao's blog post on the PFR formalistion. It's a graph where the nodes represent different definitions, lemmas and theorems in the formalisation. The colour indicates the status of the formalisation. Green means that it is proven; light blue means that they can be stated but have not been proven, and the remaining nodes (black here) are those that can not even be written down yet (they might be require some definitions to be written down first). The reason this is exc ... Read full article.