Mathlib Map

Theorems · Definition · order theory

LowerSet.Iio

{α : Type u_1} → [inst : Preorder α] → α → LowerSet α

Strict principal lower set. Set.Iio as a lower set.

Defined in
Mathlib.Order.UpperLower.Principal
Cited by
7 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LowerSet.map_Iio · cited by 0LowerSet.map_IioLowerSet.coe_Iio · cited by 0LowerSet.coe_IioLowerSet.mem_Iio_iff · cited by 0LowerSet.mem_Iio_iffLowerSet.Iio_bot · cited by 0LowerSet.Iio_botLowerSet.Iio_eq_bot · cited by 0LowerSet.Iio_eq_botLowerSet.Iio_strictMono · cited by 0LowerSet.Iio_strictMonoLowerSet.Ioi_le_Ici · cited by 0LowerSet.Ioi_le_IciPreorder · cited by 7952PreorderSet.Iio · cited by 1166Set.IioLowerSet · cited by 230LowerSetisLowerSet_Iio · cited by 3isLowerSet_IioLowerSet.IioCITED BYCITES

Cites4

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

Cited by7

Results whose statement or proof uses this declaration.