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In this work, we describe our experience in learning the use of a computerproof assistant - specifically, Lean - from scratch, through proving formulaefor the solutions of polynomial equations. Specifically, in this work wecharacterize the solutions of quadratic, cubic, and quartic polynomials overcertain fields, specifically, fields with operations returning square and cubicroots of characteristic other than two or three. The purpose of this work isthus twofold. Firstly, it describes the learning experience of a starting Leanuser, including a detailed comparison between our work in Lean and very closelyrelated work in Coq. Secondly, our results represent a modest improvement overthe aforementioned related work in Coq, which we hope will be of somescientific interest.

The solutions to single-variable polynomials, implemented and verified in Lean