Theorems · Definition · order theory
Finset.Ico
{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.Ico a b as a
finset.
- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 450 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.finsetIcoproof · cited by 1
Cited by459
Results whose statement or proof uses this declaration.
- Nat.divisorsproof · cited by 137
- Finset.coe_Icostatement · cited by 66
- Nat.properDivisorsproof · cited by 52
- Finset.mem_Icostatement · cited by 50
- Multiset.Icoproof · cited by 32
- Finset.range_eq_Icostatement · cited by 26
- Nat.Ico_zero_eq_rangestatement and proof · cited by 25
- Finset.Ico_eq_empty_of_lestatement · cited by 22
- Nat.mem_divisorsproof · cited by 22
- Nat.card_Icostatement · cited by 19
- SummationFilter.symmetricIcoproof · cited by 17
- Nat.mem_properDivisorsproof · cited by 15
Showing the 200 most cited of 459.