Theorems · Theorem · logic and foundations
Cardinal.bddAbove_iff_small
∀ {s : Set Cardinal.{u}}, BddAbove s ↔ Small.{u, u + 1} ↑sA set of cardinals is bounded above iff it's small, i.e. it corresponds to a usual ZFC set.
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Equiv.symmproof · cited by 3,681
- Cardinalstatement and proof · cited by 2,598
- BddAbovestatement and proof · cited by 620
- Smallstatement and proof · cited by 369
- Equiv.symm_apply_applyproof · cited by 320
- upperBoundsproof · cited by 263
- Cardinal.sumproof · cited by 58
- Small.casesOnproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.bddAbove_of_smallproof · cited by 37
- Cardinal.bddAbove_imageproof · cited by 4
- not_small_cardinalproof · cited by 0