Theorems · Theorem · logic and foundations
Ordinal.bddAbove_iff_small
∀ {s : Set Ordinal.{u}}, BddAbove s ↔ Small.{u, u + 1} ↑s- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Ordinalstatement and proof · cited by 1,688
- BddAbovestatement and proof · cited by 620
- Smallstatement and proof · cited by 369
- upperBoundsproof · cited by 263
- Ordinal.bddAbove_of_smallproof · cited by 19
- small_subsetproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.bddAbove_imageproof · cited by 1
- Ordinal.not_bddAbove_compl_of_smallproof · cited by 0