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Theorems · Definition · logic and foundations

ZFSet.powersetEquiv

(x : ZFSet.{u}) → ↥x.powerset ≃ ↑(𝒫 ↑x)

ZFSet.powerset is equivalent to Set.powerset.

Defined in
Mathlib.SetTheory.ZFC.Basic
Cited by
1 results in Mathlib
Foundations
Depth 28 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.

ZFSet.card_powerset · cited by 1ZFSet.card_powersetSet · cited by 53352SetEquiv · cited by 8337EquivSetLike.coe · cited by 8199SetLike.coeSet.Elem · cited by 7166Set.ElemZFSet · cited by 259ZFSetSet.powerset · cited by 67Set.powersetZFSet.powerset · cited by 11ZFSet.powersetZFSet.sep · cited by 8ZFSet.sepZFSet.powersetEquivCITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.