Mathlib Map

Theorems · Definition · order theory

RelIso.toInitialSeg

{α : Type u_1} → {β : Type u_2} → {r : α → α → Prop} → {s : β → β → Prop} → r ≃r s → InitialSeg r s

A relation isomorphism is an initial segment embedding

Defined in
Mathlib.Order.InitialSeg
Cited by
4 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
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Around this declaration

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

PrincipalSeg.transRelIso · cited by 3PrincipalSeg.transRelIsoOrderIso.toInitialSeg · cited by 3OrderIso.toInitialSegInitialSeg.refl · cited by 2InitialSeg.reflInitialSeg.eq_relIso · cited by 1InitialSeg.eq_relIsoOrdinal.lift_type_le · cited by 1Ordinal.lift_type_leRelIso.toInitialSeg_toFun · cited by 0RelIso.toInitialSeg_toFunOrdinal.lift_type_lt · cited by 0Ordinal.lift_type_ltInitialSeg.total · cited by 0InitialSeg.totalRelIso · cited by 456RelIsoInitialSeg · cited by 70InitialSegRelIso.toRelEmbedding · cited by 34RelIso.toRelEmbeddingRelIso.toInitialSegCITED BYCITES

Cites3

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

Cited by8

Results whose statement or proof uses this declaration.