Theorems · Theorem · logic and foundations
Ordinal.bddAbove_of_small
∀ {s : Set Ordinal.{u}} [Small.{u, u + 1} ↑s], BddAbove s- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Cardinalproof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- le_of_ltproof · cited by 1,175
- Order.succproof · cited by 633
- BddAbovestatement · cited by 620
- Set.mem_image_of_memproof · cited by 371
- Smallstatement and proof · cited by 369
- Cardinal.ordproof · cited by 266
- upperBoundsproof · cited by 263
Cited by19
Results whose statement or proof uses this declaration.
- Ordinal.le_iSupproof · cited by 19
- Ordinal.iSup_le_iffproof · cited by 9
- Ordinal.isNormal_derivFamilyproof · cited by 5
- Ordinal.nfpFamily_fpproof · cited by 4
- Ordinal.lt_iSup_iffproof · cited by 4
- Ordinal.lift_cof_iSup_add_oneproof · cited by 4
- Ordinal.derivFamily_fpproof · cited by 3
- Ordinal.apply_omega0_of_isNormalproof · cited by 2
- Ordinal.bddAbove_iff_smallproof · cited by 2
- Ordinal.lsub_le_of_range_subsetproof · cited by 1
- Ordinal.IsNormal.bsupproof · cited by 1
- Ordinal.add_iSupproof · cited by 1