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For many years, I have been interested in introducing students to thedevelopment of complex systems by means of modelling and refinement. To thisend, I did not find anything better than presenting many examples of systemdevelopments. However, I figured out that my examples were not explicit enoughon how (mechanical) proofs are performed. So, besides courses presenting theseexamples and also some courses in various forms of proofs (propositionalcalculus, first order predicate calculus, set theory), I decided to study thework of professional mathematicians, thinking that it could be good examplesfor students. Among the works I already studied and reconstructed are thetheorem of Zermelo, the theorem of Cantor-Bernstein, the planar graph theoremof Kuratowski, the topological proof of the infinity of primes of Furstenberg,the intermediate value theorem of Bolzano, the Archimedean property of the setof Real numbers, and others. More recently, I found that the Goodstein theoremwas also very interesting. The purpose of this short note is to give someinformation about this theorem and the way I introduce a weak form of it tostudents.

Formal Proof of the Weak Goodstein Theorem