Theorems · Theorem · logic and foundations
Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite
∀ {α : Type u_1} {s : Set α}, s.Infinite → ∃ t u, t ∪ u = s ∧ Disjoint t u ∧ Cardinal.mk ↑t = Cardinal.mk ↑u- Defined in
- Mathlib.Data.Set.Card.Arithmetic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivproof · 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.rangeproof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Disjointstatement · cited by 2,201
- Cardinal.mkstatement and proof · cited by 942
- Infiniteproof · cited by 352
- Set.image_univproof · cited by 322
Cited by1
Results whose statement or proof uses this declaration.
- Set.exists_union_disjoint_cardinal_eq_of_evenproof · cited by 2