Theorems · Theorem · logic and foundations
Cardinal.mk_preimage_down
∀ {α : Type u} {s : Set α}, Cardinal.mk ↑(ULift.down ⁻¹' s) = Cardinal.lift.{v, u} (Cardinal.mk ↑s)- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.Elemstatement and proof · cited by 7,166
- Set.preimagestatement and proof · cited by 4,946
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Function.Bijectiveproof · cited by 863
- Cardinal.liftstatement · cited by 583
- Set.restrictPreimageproof · cited by 84
- Equiv.ofBijectiveproof · cited by 70
- Function.Bijective.compproof · cited by 26
- Cardinal.eqproof · cited by 17
- ULift.up_bijectiveproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.mk_subtype_le_of_countable_eventually_memproof · cited by 1