[Merged by Bors] - feat(data/set/ncard): noncomputable set cardinality #18576
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eric-wieser
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| ({a} : set α).ncard = 1 := | ||
| by simp [ncard_eq_to_finset_card] | ||
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| lemma ncard_singleton_inter : ({a} ∩ s).ncard ≤ 1 := |
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Might be best to first prove a subsingleton set has cardinality ≤1, then use that a subsingleton subset is a subsingleton.
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alexjbest
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riccardobrasca
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LGTM, thanks!
Let's just wait for @kmill to have a look (who knows finite set in Lean better than me).
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I think it's reasonable to merge this, we can always change it later if needed, thanks! bors merge |
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This PR introduces a function `set.ncard` that (noncomputably) gives the cardinality of a finite `set`, or zero if the set is infinite. The intention is to give a way to reason about set cardinality that avoids data and going between `set` and `finset`. This is especially useful for reasoning about sets in a `finite` type. The added file is somewhat large, but it is essentially just duplicating the API in `data.finset.card` (minus the induction lemmas). Co-authored-by: Peter Nelson <71660771+apnelson1@users.noreply.github.com>
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This PR introduces a function
set.ncardthat (noncomputably) gives the cardinality of a finiteset, or zero if the set is infinite. The intention is to give a way to reason about set cardinality that avoids data and going betweensetandfinset. This is especially useful for reasoning about sets in afinitetype.The added file is somewhat large, but it is essentially just duplicating the API in
data.finset.card(minus the induction lemmas).