Theorems · Definition · logic and foundations
Ordinal.ToType.mk
{o : Ordinal.{u_1}} → ↑(Set.Iio o) ≃o o.ToTypeThe order isomorphism between ordinals less than o and o.ToType.
- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Ordinalstatement and proof · cited by 1,688
- Set.Iiostatement and proof · cited by 1,166
- OrderIsostatement · cited by 874
- Ordinal.ToTypestatement and proof · cited by 143
- PrincipalSeg.toRelEmbeddingproof · cited by 129
- Ordinal.typeinproof · cited by 60
- Ordinal.enumproof · cited by 39
- Ordinal.typein_lt_selfproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- Ordinal.ToType.toOrdproof · cited by 8
- Ordinal.typein_ordinalproof · cited by 3
- Cardinal.mk_biUnion_le_of_le_liftproof · cited by 3
- Ordinal.lift_card_iSup_le_sum_cardproof · cited by 2
- Ordinal.mem_toPSet_iffproof · cited by 1
- Ordinal.card_iSup_Iio_le_sum_cardproof · cited by 1
- Ordinal.rank_toPSetproof · cited by 1
- Ordinal.exists_isFundamentalSeqproof · cited by 1
- Ordinal.ToType.mk_applystatement and proof · cited by 0
- Ordinal.ToType.mk_symm_apply_coestatement and proof · cited by 0
- Ordinal.card_iSup_Iio_le_card_mul_iSupproof · cited by 0