Yeah, I would say that understanding conjectures often requires knowing some "background lemmas" in addition to knowing the definitions of the objects used in t

Yeah, I would say that understanding conjectures often requires knowing some "background lemmas" in addition to knowing the definitions of the objects used in the definition, for this very reason. As another very simple example it can be shown that you can replace ℕ by the set of integers greater than 3, and the resulting conjecture is equivalent.