Theorems · Definition · order theory
OrderIso.trans
{α : Type u_2} →
{β : Type u_3} → {γ : Type u_4} → [inst : LE α] → [inst_1 : LE β] → [inst_2 : LE γ] → α ≃o β → β ≃o γ → α ≃o γComposition of two order isomorphisms is an order isomorphism.
- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- OrderIsostatement and proof · cited by 874
- RelIso.transproof · cited by 18
Cited by58
Results whose statement or proof uses this declaration.
- Cardinal.preAlephproof · cited by 44
- Real.tanOrderIsoproof · cited by 10
- PrimeSpectrum.isIdempotentElemEquivClopensproof · cited by 10
- Real.sinOrderIsoproof · cited by 9
- StrictMono.orderIsoOfSurjectiveproof · cited by 8
- PrimeSpectrum.primesOverOrderIsoFiberproof · cited by 8
- Finset.orderIsoOfFinproof · cited by 7
- IsCyclotomicExtension.Rat.subgroupGalEquivSubgroupCharproof · cited by 6
- OrderIso.sumLexIicIoiproof · cited by 6
- OrderIso.sumLexIioIciproof · cited by 6
- IsGaloisGroup.intermediateFieldEquivSubgroupproof · cited by 6
- MulChar.subgroupOrderIsoSubgroupMulCharproof · cited by 6