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Theorems · Theorem · logic and foundations

Set.powerset_empty

∀ {α : Type u}, 𝒫 ∅ = {∅}
Defined in
Mathlib.Data.Set.Basic
Cited by
3 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopologicalSpace.vietoris.isClopen_singleton_empty · cited by 2vietoris.isClopen_singlet…Filter.smallSets_bot · cited by 2Filter.smallSets_botUniformSpace.hausdorff.isClopen_singleton_empty · cited by 2hausdorff.isClopen_single…Set · cited by 53352SetSet.ext · cited by 2266Set.extSet.powerset · cited by 67Set.powersetSet.subset_empty_iff · cited by 40Set.subset_empty_iffSet.powerset_emptyCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.