Theorems · Definition · order theory
PrincipalSeg.relIsoTrans
{α : Type u_1} →
{β : Type u_2} →
{γ : Type u_3} →
{r : α → α → Prop} → {s : β → β → Prop} → {t : γ → γ → Prop} → r ≃r s → PrincipalSeg s t → PrincipalSeg r tComposition of an order isomorphism with a principal segment embedding, as a principal segment embedding
- Defined in
- Mathlib.Order.InitialSeg
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RelIsostatement and proof · cited by 456
- PrincipalSeg.toRelEmbeddingproof · cited by 129
- PrincipalSegstatement and proof · cited by 73
- PrincipalSeg.topproof · cited by 41
- RelIso.toRelEmbeddingproof · cited by 34
- RelEmbedding.transproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- InitialSeg.transPrincipalproof · cited by 2
- PrincipalSeg.relIsoTrans_applystatement · cited by 1
- PrincipalSeg.top_eqproof · cited by 0
- PrincipalSeg.relIsoTrans_topstatement · cited by 0
- Ordinal.lift_type_ltproof · cited by 0