Mathlib Map

Theorems · Definition · order theory

PartialOrder.lift

{α : Type u_2} → {β : Type u_3} → [PartialOrder β] → (f : α → β) → Function.Injective f → PartialOrder α

Transfer a PartialOrder on β to a PartialOrder on α using an injective function f : α → β. See also Function.Injective.partialOrder when only the proof fields need to be transferred. See note [reducible non-instances].

Defined in
Mathlib.Order.Basic
Cited by
1 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
PartialOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

specializationOrder · cited by 3specializationOrdercompare_of_injective_eq_compareOfLessAndEq · cited by 0compare_of_injective_eq_c…PartialOrder.ofSetLike · cited by 0PartialOrder.ofSetLikePartialOrder · cited by 6410PartialOrderFunction.Injective.partialOrder · cited by 0Injective.partialOrderPartialOrder.liftCITED BYCITES

Cites2

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.