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Theorems · Theorem · logic and foundations

Cardinal.mk_powerset

∀ {α : Type u} (s : Set α), Cardinal.mk ↑(𝒫 s) = 2 ^ Cardinal.mk ↑s

A variant of Cardinal.mk_set expressed in terms of a Set instead of a Type.

Defined in
Mathlib.SetTheory.Cardinal.Order
Cited by
4 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

IsClosed.two_pow_mk_le_two_pow_mk_dense · cited by 2IsClosed.two_pow_mk_le_tw…Cardinal.mk_bounded_subset · cited by 1Cardinal.mk_bounded_subsetZFSet.card_powerset · cited by 1ZFSet.card_powersetSet.ncard_powerset · cited by 0Set.ncard_powersetSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalCardinal.mk · cited by 942Cardinal.mkSet.powerset · cited by 67Set.powersetCardinal.mk_congr · cited by 55Cardinal.mk_congrCardinal.mk_set · cited by 3Cardinal.mk_setEquiv.Set.powerset · cited by 2Set.powersetCardinal.mk_powersetCITED BYCITES

Cites8

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Cited by4

Results whose statement or proof uses this declaration.