The word of "occurrence" in terms is useful to explain notions intuitively, which frequently leads proofs into ambiguous and inaccurate ones. With theorem provers on the computer like Isabelle, however, we can handle the proofs strictly and maybe complicatedly. In the archive I show, I proved notions of the lambda calculus on the computer especially about alpha-equivalence(s) handling with occurrences.
The second merit was that though I was lacking confidence about mathematics, I could affirm my proofs were correct because of theorem provers. However, I originally proved the proofs in Isabelle before 1998. When I have proved originally, I certainly have comprehended what I did. Now, I almost don't recognize what I do, but I rewrite the legacy proofs into the present style of the Isabelle2015. Though, I often consider proofs partly when rewriting leads to failure. I can't prove in the recommended style of Isar structured proof, but prove in the style of "apply ... done" proofs with tactics and tacticals.
The proofs about alpha-equivalence(s) of the lambda calculus include the proof of correspondence between the definition of alpha-equivalence using occurrences and that using inductive set, and proofs about connection of the usual notation and de Bruijn notation.