@MISC{Rudnicki96anote, author = {Piotr Rudnicki and Andrzej Trybulec}, title = {A Note on "How to Write a Proof"}, year = {1996} }

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Abstract

We believe that mechanical checking of real-life proofs can become practical and therefore we use Mizar -- a proof checking system for proofs written in a style of traditional mathematics. In the beginning of 1994 we came across a copy of L. Lamport's [8] paper in which "a method for writing proofs is proposed that makes it much harder to prove things that are not true." For Mizar users the issue of How to Write a Proof? is an important one, as Mizar is a proof checker and not an automated prover. We have tested Mizar fitness for writing structured proofs in Lamport's style by rewriting his proof of the irrationality of p 2 into Mizar. It was not surprising to notice that formatting conventions help in presenting and reading proofs. However, such conventions do not, as they cannot, guarantee the correctness of the written proof, our little test being a case in point. We advocate development and employment of mechanical checkers for proofs.