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Theorems · Theorem · order theory

Set.finite_iUnion_of_subsingleton

∀ {α : Type u} {ι : Sort u_1} [Subsingleton ι] {s : ι → Set α}, (⋃ i, s i).Finite ↔ ∀ (i : ι), (s i).Finite
Defined in
Mathlib.Data.Set.Finite.Lattice
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Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Subsingleton
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Set · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredSet.Nonempty · cited by 2627Set.NonemptySet.iUnion · cited by 2483Set.iUnionSet.Finite · cited by 1814Set.FiniteSubsingleton.pairwise · cited by 3Subsingleton.pairwiseSet.finite_iUnion_iff · cited by 2Set.finite_iUnion_iffSet.iUnion_plift_down · cited by 1Set.iUnion_plift_downSet.finite_iUnion_of_subsingl…CITED BYCITES

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