Formal and Natural Proof - A phenomenological approach

It is frequently claimed (see e.g. [Rav]) that the formalization of a mathematical proof requires a quality of understanding that subsumes all necessary acts for checking the proof and that, consequently, automatic proof checking cannot lead to an epistemic gain about a proof. We present a project developing what is sometimes called a ’fortified formalism’ and argue taking a phenomenological look at proof understanding, that proofs can be (and often are) given in a way that allows a formalization sufficient for producing an automatically checkable writeup, but does not subsume