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Theorems · Definition · order theory

OrderIso.toInitialSeg

{α : Type u_1} → {β : Type u_2} → [inst : Preorder α] → [inst_1 : Preorder β] → α ≃o β → α ≤i β

An order isomorphism is an initial segment

Defined in
Mathlib.Order.InitialSeg
Cited by
3 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cardinal.lift_preAleph · cited by 2Cardinal.lift_preAlephOrderIso.isNormal · cited by 2OrderIso.isNormalOrderIso.toInitialSeg_toFun · cited by 0OrderIso.toInitialSeg_toF…Preorder · cited by 7952PreorderOrderIso · cited by 874OrderIsoInitialSeg · cited by 70InitialSegOrderIso.toRelIsoLT · cited by 9OrderIso.toRelIsoLTRelIso.toInitialSeg · cited by 4RelIso.toInitialSegOrderIso.toInitialSegCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.