Kleiner, 1991). Today the universally accepted definition is that a proof is a finite sequence of propositions, each of which is an axiom or follows from preceding propositions by the rules of logical inference [...] they often have the advantage of conveying greater insight and understanding. Not all practicing mathematicians, however, are content with such informal proofs and “comfortable that the idea works” (Thurston [...] along with their growing use as tools in mathematics practice, has facilitated this trend. The paper will describe the development of these tools over time, showing how proof checking through formalization
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