Theorems · Definition · order theory
Set.Ioi
{α : Type u_1} → [Preorder α] → α → Set αIoi a is the left-open right-infinite interval $(a, ∞)$.
- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 1,463 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 7 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
Cited by1,517
Results whose statement or proof uses this declaration.
- measurableSet_Ioistatement · cited by 83
- Set.mem_Ioistatement · cited by 80
- tendsto_orderproof · cited by 60
- isOpen_Ioistatement · cited by 43
- interior_Iccproof · cited by 37
- Filter.Ioi_mem_atTopstatement and proof · cited by 36
- BoxIntegral.IntegrationParams.MemBaseSetstatement · cited by 34
- Set.Ioi_subset_Ici_selfstatement and proof · cited by 34
- mellinproof · cited by 33
- Finset.coe_Ioistatement · cited by 28
- Set.Ioi_subset_Ioistatement and proof · cited by 28
- Ioi_mem_nhdsstatement · cited by 27
Showing the 200 most cited of 1,517.