Hi all, see 59803048b0e8 for some basic facts about almost everywhere bijections aka permutations. Maybe this will become a convenient coagulation point for various scattered material in the future. It turned out quite ambitious to formulate basic properties, e.g. circularity. I did not search for any literature because I thought that things covered in introductory courses should be straightforward to formalize ;-). My original interest had been cycles, but I realized that this needs more work than I am willing to spend here, even more since I further realized that the combinatorial interpretation of first Stirling numbers can work just on cycles without need of their interpretation as permutations. If anybody wants to push that work further, the agenda is roughly as follows: * Consolidate scattered material on permutations (functions) into Library/Perm.thy (see my post https://lists.cam.ac.uk/pipermail/cl-isabelle-users/2016-June/msg00091.html for further details). * Gradually abandon Library/Permutation with its equivalence relation ‹perm› – it is much easier to reason about equality on multisets ‹mset xs = mset ys›. There is also no equivalence relation ‹same_elems :: 'a list ⇒ 'a list ⇒ bool›, but we write just ‹set xs = set ys›, for the same and good reason.
I still have some work regarding cycles and combinatorial functions in the drawer which I hope to finish gradually over time. Cheers, Florian -- PGP available: http://isabelle.in.tum.de/~haftmann/pgp/florian_haftmann_at_informatik_tu_muenchen_de
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