More succinctly: The thing you want proven is a proposition. A proposition is a type. Writing the algorithm which implements the type is the same as proving it

More succinctly: The thing you want proven is a proposition. A proposition is a type. Writing the algorithm which implements the type is the same as proving it. https://ncatlab.org/nlab/show/propositions+as+types https://ncatlab.org/nlab/show/propositions+as+types