SC
You said "The IR is not a subset of the CPL. They are both different subsets of the ATPL."
If the IR subjects are not a subset of the CPL, then there must be some topics in the IR syllabus that aren't in the CPL syllabus. This doesn't seem correct to me (but I'm not a lecturer) because passing the CPL (or ATPL) exams is an alternative to passing the IR exams to satisfy the "written" part of the requirements for the issue of an instrument rating.
Indeed, at present, the CPL or ATPL route is the only one available as no organisation has yet run a course for the JAA IR examinations.
So if you are a lecturer, what is in the IR syllabus that isn't in the CPL syllabus?