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.
Hint
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'.
Solution
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Pierre Castéran