More on permutations

Consider the notion of permutation as defined in that exercise
Build a couterexample, with two lists l and l' of the same length, such that the proposition perm l l' holds. Prove this proposition.


Consider lists on nat or Z, or any type suitable for defining a function which counts the number of occurrences of any item in a list. Then prove and apply a lemma stating that if l' is a permutation of l, then this function always returns the same value when applied to l or l'.


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Pierre Castéran