Comment by franklin_p_dyer

Really cool post! This is an awesome idea and I'd love to see more of these. :-)

Maybe these won't be the kind of thing you are looking for, but here are some gems that would be cool to see formalized, some of which I've been meaning to do myself someday:

- There are many parts of the book "A Course in Constructive Algebra" (Mines, Richman, Ruitenburg) worthy of being formalized, but even just the discussion of "omniscience principles" in the first chapter would be cool.

- I absolutely love Sierpinski's book "Cardinal and Ordinal Numbers", and although I'm not sure it would be considered a book of "intuitionistic mathematics", he is careful enough about pointing out where he uses AoC for parts of his book to be suitable for consideration. The results and exercises in VI.5 "Axiom of choice for finite sets" are probably my favorite in the whole book and would be awesome to see formalized.

- Tarski's Theorem about Choice: https://en.wikipedia.org/wiki/Tarski%27s_theorem_about_choic..., particularly from Tarski's original paper (though it is in French).

- I am not sure about a historical article/source for this one, but formalization of some results about Dedekind-finite and Dedekind-infinite sets (https://en.wikipedia.org/wiki/Dedekind-infinite_set) could be really fun. I find these to be very counterintuitive.