Incremental View Maintenance for projection

I was reading https://www2.cs.duke.edu/courses/spring02/cps296.1/lectures/08-view.pdf

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Or in the paper “Incremental Maintenance of Views with Duplicates,” by Griffin and Libkin, SIGMOD, 1995. figure 2. enter image description here

I don’t understand why we need to min(R,ΔR) before -. Is there any counterexample?