Theorems · Definition · order theory
Finset.Ioc
{α : Type u_1} → [inst : Preorder α] → [LocallyFiniteOrder α] → α → α → Finset αThe finset $(a, b]$ of elements x such that a < x and x ≤ b. Basically Set.Ioc a b as a
finset.
- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 301 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 5 definitions · uses no axioms
- Assumes
- PreorderLocallyFiniteOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- LocallyFiniteOrder.finsetIocproof · cited by 1
Cited by312
Results whose statement or proof uses this declaration.
- Finset.coe_Iocstatement and proof · cited by 55
- Chebyshev.thetaproof · cited by 38
- schnirelmannDensityproof · cited by 35
- Chebyshev.psiproof · cited by 34
- Finset.mem_Iocstatement · cited by 26
- IicProdIocstatement and proof · cited by 20
- Finset.Ioc_subset_Iic_selfstatement · cited by 12
- Multiset.Iocproof · cited by 11
- MeasurableEquiv.piSingletonstatement and proof · cited by 10
- measurable_IicProdIocstatement and proof · cited by 9
- Finset.left_notMem_Iocstatement and proof · cited by 8
- Chebyshev.psi_eq_zero_of_lt_twoproof · cited by 7
Showing the 200 most cited of 312.