# Merging states in LALR parser

I was learning LALR parsers from the dragon book (Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman) and I came across the example on page 267. I'll try my best to describe my question without needing the actual book for reference.

The book states that:

I4 and I7 form such a pair, with core $$\{C -> d.\}$$ . Similarly, I3 and I6 form another pair, with core $$\{C -> c.C, C -> .cC, C -> .d\}$$ . There is one more pair, I8 and I9 with common core $$\{C -> cC.\}$$ .

Here, I3 and I6 have the same set of cores $$\{C -> c.C, C -> .cC, C -> .d\}$$ . My question is, should I combine I3 and I6 if I3 had the set of cores $$\{C -> c.C, C -> .cC\}$$ and I6 had the set of cores $$\{C -> c.C, C -> .cC, C -> .d\}$$ ? That is, should the set of cores for the itemsets should be exactly the same for combining them or can one be a proper subset of the other?