feat(data/list/nodup_permutations): nodup_permutations #8494
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Provide explicit embedding from a subtype of a disjuction into a sum type. If the disjunction is disjoint, upgrade to an equiv. Additionally, provide `subtype.imp_embedding`, lowering a subtype along an implication.
…of one element Additionally, a lemma proving that the cardinality of such a subtype is 1.
Using a cardinality argument, prove that the list of permutations of a list is nodup if the list is nodup. TODO: prove the reverse implication. Implementation: provide an explicit equiv between the perm Prop and the equiv over indices. TODO: prove that this equiv moves indices as expected TODO: generalize to sublists/embeddings
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This reverts commit 4d8c0b0.
this prevents needing to infer an additional instance in rewrites
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This was referenced Aug 9, 2021
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Closed in favor of #8616 |
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Aug 18, 2021
A simpler version of #8494 TODO: `nodup s.permutations ↔ nodup s` TODO: `count s s.permutations = (zip_with count s s.tails).prod` Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com>
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Using a cardinality argument, prove that the list of permutations of a list
is nodup if the list is nodup.
TODO: prove the reverse implication.
Implementation: provide an explicit equiv between
the perm Prop and the equiv over indices.
TODO: prove that this equiv moves indices as expected
TODO: generalize to sublists/embeddings