Theorems · Theorem · logic and foundations
Ordinal.iSup_eq_lsub_iff
Deprecated since 2026-03-27Mathlib marks this declaration as deprecated.
∀ {ι : Type u_3} (f : ι → Ordinal.{max u_4 u_3}),
iSup f = Ordinal.lsub f ↔ ∀ a < Ordinal.lsub f, Order.succ a < Ordinal.lsub f- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- le_antisymmproof · cited by 2,068
- Ordinalstatement and proof · cited by 1,688
- LT.lt.neproof · cited by 872
- Order.succstatement and proof · cited by 633
- le_of_eqproof · cited by 366
- LT.lt.falseproof · cited by 66
- Order.lt_succproof · cited by 45
- Ordinal.lsubstatement and proof · cited by 43
- Ordinal.le_iSupproof · cited by 19
- Ordinal.lsub_leproof · cited by 6
- Ordinal.lsub_le_iffproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.bsup_eq_blsub_iff_succproof · cited by 0