Theorems · Theorem · logic and foundations
Ordinal.succ_iSup_le_lsub_iff
Deprecated since 2026-03-27Mathlib marks this declaration as deprecated.
∀ {ι : Type u_3} (f : ι → Ordinal.{max u_4 u_3}), Order.succ (iSup f) ≤ Ordinal.lsub f ↔ ∃ i, f i = iSup f- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- LT.lt.neproof · cited by 872
- Order.succstatement and proof · cited by 633
- LE.le.antisymmproof · cited by 507
- Ordinal.lsubstatement and proof · cited by 43
- LE.le.lt_iff_neproof · cited by 34
- Order.succ_le_iffproof · cited by 20
- Ordinal.le_iSupproof · cited by 19
- Ordinal.lt_lsubproof · cited by 7
- Ordinal.lsub_leproof · cited by 6
- Ordinal.iSup_le_lsubproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.succ_iSup_eq_lsub_iffproof · cited by 1