A case-study in algebraic manipulation using mechanized reasoning tools

In this article, two different mechanized reasoning tools (Coq and Isabelle/HOL) are used in order to prove some basic but significant properties extracted from a symbolic computation system called Kenzo. In particular, we focused on a property called 'cancellation theorem', which can be applied to the proof of the idempotence property of a differential morphism. This result is used as a case-study to compare the capabilities and styles of the two proof assistants. The conclusion of our comparison is that both tools are adequate to solve the case-study presented in this article in a rather similar way but depending on their specific styles. This research is part of a more general project devoted to increase the reliability of computer algebra systems for calculations in algebraic topology.