Theorems · Definition · order theory
Set.Ioo
{α : Type u_1} → [Preorder α] → α → α → Set αIoo a b is the left-open right-open interval $(a, b)$.
- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 1,214 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 8 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 by1,244
Results whose statement or proof uses this declaration.
- Set.uIooproof · cited by 68
- Set.Ioo_subset_Icc_selfstatement · cited by 54
- isOpen_Ioostatement · cited by 54
- Finset.coe_Ioostatement · cited by 48
- measurableSet_Ioostatement · cited by 42
- AkraBazziRecurrence.GrowsPolynomiallyproof · cited by 41
- interior_Iccstatement and proof · cited by 37
- Set.Ioo_subset_Ioc_selfstatement · cited by 30
- Set.mem_Ioostatement · cited by 29
- Set.Ioo_subset_Ico_selfstatement · cited by 29
- Ioo_mem_nhdsstatement · cited by 27
- Affine.Simplex.interiorproof · cited by 26
Showing the 200 most cited of 1,244.