Theorems · Definition · logic and foundations
Ordinal.enumOrdOrderIso
(s : Set Ordinal.{u_1}) → ¬BddAbove s → Ordinal.{u_1} ≃o ↑sAn order isomorphism between an unbounded set of ordinals and the ordinals.
- Defined in
- Mathlib.SetTheory.Ordinal.Enum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 7,166
- Ordinalstatement and proof · cited by 1,688
- OrderIsostatement · cited by 874
- BddAbovestatement and proof · cited by 620
- Ordinal.enumOrdproof · cited by 23
- Ordinal.enumOrd_strictMonoproof · cited by 10
- StrictMono.orderIsoOfSurjectiveproof · cited by 8
- Ordinal.enumOrd_memproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.preAlephproof · cited by 44
- Ordinal.enumOrd_isNormal_iff_isClosedproof · cited by 0