Theorems · Theorem · logic and foundations
Ordinal.iSup_typein_limit
Deprecated since 2026-03-27Use Order.IsSuccPrelimit.sSup_Iio instead.
∀ {o : Ordinal.{u}}, (∀ a < o, Order.succ a < o) → iSup ⇑(Ordinal.typein fun x1 x2 => x1 < x2).toRelEmbedding = o- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- iSupstatement · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- SupSet.sSupproof · cited by 954
- Order.succstatement and proof · cited by 633
- RelEmbeddingstatement · cited by 281
- Order.IsSuccPrelimitproof · cited by 157
- Ordinal.ToTypestatement and proof · cited by 143
- PrincipalSeg.toRelEmbeddingstatement and proof · cited by 129
- Ordinal.typeinstatement and proof · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.bsup_id_limitproof · cited by 1