  Diproche ("Didactical Proof Checking") is an automatic system for supporting
the acquistion of elementary proving skills in the initial phase of university
education in mathematics. A key feature of Diproche - which is designed by the
example of the Naproche system developed by M. Cramer and others - is an
automated proof checker for proofs written in a controlled fragment of natural
language specifically designed to capture the language of beginners' proving
exercises in mathematics. Both the accepted language and proof methods depend
on the didactical and mathematical context and vary with the level of education
and the topic proposed. An overall presentation of the system in general was
given in Carl and Krapf 2019. Here, we briefly recall the basic architecture of
Diproche and then focus on explaining key features and the working principles
of Diproche in the sample topics of elementary number theory and axiomatic
geometry.
