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De Bruijn indices are great, I use them to construct what I call the "De Bruijn Abstraction Algebra"; it comes in two forms, one is used to give a characterisation of alpha equivalence for abstraction algebra, the other one is used to prove completeness of abstraction logic. It is described in [1], and I have described and proven correct everything in excruciating detail. That makes it quite a tough read, although in the end, it is elementary and simple.

[1] http://abstractionlogic.com



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