Theorems · Definition · order theory
Multiset.Ico
{α : Type u_1} → [inst : Preorder α] → [LocallyFiniteOrder α] → α → α → Multiset αThe multiset of elements x such that a ≤ x and x < b. Basically Set.Ico a b as a
multiset.
- Defined in
- Mathlib.Order.Interval.Multiset
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- PreorderLocallyFiniteOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Multisetstatement · cited by 2,627
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icoproof · cited by 450
- Finset.valproof · cited by 438
Cited by32
Results whose statement or proof uses this declaration.
- Multiset.Ico_disjoint_Icostatement and proof · cited by 2
- Multiset.Ico_eq_zerostatement · cited by 1
- Multiset.Ico_eq_zero_iffstatement · cited by 1
- Nat.filter_multiset_Ico_card_eq_of_periodicstatement and proof · cited by 1
- Multiset.map_add_left_Icostatement and proof · cited by 1
- Multiset.right_notMem_Icostatement · cited by 1
- Multiset.mem_Icostatement · cited by 1
- Nat.multiset_Ico_map_modstatement and proof · cited by 1
- Multiset.Ico_eq_zero_of_lestatement · cited by 0
- Multiset.Ico_filter_lestatement and proof · cited by 0
- Multiset.Ico_filter_le_leftstatement · cited by 0
- Multiset.Ico_filter_le_of_le_leftstatement · cited by 0