Theorems · Definition · order theory
Set.Ioc
{α : Type u_1} → [Preorder α] → α → α → Set αIoc a b is the left-open right-closed interval $(a, b]$.
- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 971 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 11 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 by993
Results whose statement or proof uses this declaration.
- intervalIntegralproof · cited by 546
- IntervalIntegrableproof · cited by 316
- Set.uIocproof · cited by 182
- intervalIntegral.integral_of_lestatement and proof · cited by 83
- measurableSet_Iocstatement · cited by 65
- Finset.coe_Iocstatement · cited by 55
- Set.Ioc_subset_Icc_selfstatement · cited by 53
- Set.Ioc_eq_emptystatement and proof · cited by 38
- Set.uIoc_of_lestatement and proof · cited by 38
- intervalIntegral.integral_symmproof · cited by 35
- intervalIntegral.integral_sameproof · cited by 31
- Set.Ioo_subset_Ioc_selfstatement · cited by 30
Showing the 200 most cited of 993.