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Thomas Eckl uses worksheets like this to try to ensure that students understand the meaning, rather than just remember the wording, of theorems in lectures. The idea is that the "rules" which students are asked to establish on the worksheet are formulated in a different way from the statements of theorems in lectures, so that students need to understand the theorem statements in order to establish the rules.
He did part of the worksheet during a lecture, animating the students to collect the relevant facts from the lecture and connect them with a little argument if necessary. Some students managed well, others needed a lot of help.
He didn't ask students to submit their solutions, but had the impression from the exam that the worksheet at least helped the students to recall the rules.