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Diproche ("Didactical Proof Checking") is an automatic system for supportingthe acquistion of elementary proving skills in the initial phase of universityeducation in mathematics. A key feature of Diproche - which is designed by theexample of the Naproche system developed by M. Cramer and others - is anautomated proof checker for proofs written in a controlled fragment of naturallanguage specifically designed to capture the language of beginners' provingexercises in mathematics. Both the accepted language and proof methods dependon the didactical and mathematical context and vary with the level of educationand the topic proposed. An overall presentation of the system in general wasgiven in Carl and Krapf 2019. Here, we briefly recall the basic architecture ofDiproche and then focus on explaining key features and the working principlesof Diproche in the sample topics of elementary number theory and axiomaticgeometry.

Number Theory and Axiomatic Geometry in the Diproche System