Theorems · Definition · order theory
PrincipalSeg.orderIsoIio
{α : Type u_1} →
{β : Type u_2} → [inst : PartialOrder α] → [inst_1 : PartialOrder β] → (f : α <i β) → α ≃o ↑(Set.Iio f.top)If f : α <i β is a principal segment, this is the induced order
isomorphism α ≃o Iio f.top.
- Defined in
- Mathlib.Order.Interval.Set.InitialSeg
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- Set.Iiostatement · cited by 1,166
- OrderIsostatement · cited by 874
- RelIso.symmproof · cited by 193
- PrincipalSegstatement and proof · cited by 73
- PrincipalSeg.topstatement · cited by 41
- OrderIso.ofRelIsoLTproof · cited by 8
- PrincipalSeg.subrelIsoproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.hasColimitsOfShape_of_isSuccLimit'proof · cited by 1
- CategoryTheory.Functor.isColimitOfIsWellOrderContinuous'proof · cited by 0
- PrincipalSeg.orderIsoIio_apply_coestatement and proof · cited by 0