Theorems · Definition · logic and foundations
Equiv.Set.powerset
{α : Type u_3} → (S : Set α) → ↑(𝒫 S) ≃ Set ↑SThe set 𝒫 S := {x | x ⊆ S} is equivalent to the type Set S.
- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.powersetstatement and proof · cited by 67
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.mk_powersetproof · cited by 4
- Set.Finite.induction_toproof · cited by 1