Reflective: I like how proving a set is a subring takes fewer axioms than proving it's a ring! I love/hate these kinds of proofs because they're usually relatively easy, but they're also tedious. The shorter set of axioms is always appreciated. :)
Difficult: At the same time, I can see myself making a mistake such as the one in the note right after Theorem 3.2; I might mistakenly make trivial assumptions (i.e. a+x=0 has a solution) instead of proving what actually needs to be proven (i.e. the solution of a+x=0 is in the set).
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