Explore derived rules in intuitionistic set theories through this insightful lecture presented as part of the Hausdorff Trimester Program: Types, Sets and Constructions. Delve into a comprehensive examination of the general machinery used to demonstrate these derived rules, gaining valuable insights into the foundations of set theory. Over the course of 42 minutes, learn from the expertise of Michael Rathjen as he unravels complex concepts and presents a thorough analysis of this fundamental aspect of mathematical logic.