[Merged by Bors] - feat: cardinality of a set with a countable cover #6351
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sgouezel
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| @@ -1389,6 +1398,16 @@ theorem card_le_of {α : Type u} {n : ℕ} (H : ∀ s : Finset α, s.card ≤ n) | |||
| exact n.lt_succ_self | |||
| #align cardinal.card_le_of Cardinal.card_le_of | |||
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| theorem card_le_of_forall_finset_subset_le {α : Type u} {n : ℕ} {t : Set α} | |||
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How about upgrading to an iff?
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Assume that a set `t` is eventually covered by a countable family of sets, all with cardinality `≤ a`. Then `t` itself has cardinality at most `a`.
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Assume that a set `t` is eventually covered by a countable family of sets, all with cardinality `≤ a`. Then `t` itself has cardinality at most `a`.
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Assume that a set `t` is eventually covered by a countable family of sets, all with cardinality `≤ a`. Then `t` itself has cardinality at most `a`.
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Assume that a set
tis eventually covered by a countable family of sets, all withcardinality
≤ a. Thentitself has cardinality at mosta.