Theorems · Definition · order theory
Multiset.Ioo
{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.Ioo a b as a
multiset.
- Defined in
- Mathlib.Order.Interval.Multiset
- Cited by
- 13 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.valproof · cited by 438
- Finset.Iooproof · cited by 185
Cited by13
Results whose statement or proof uses this declaration.
- Multiset.map_add_left_Ioostatement and proof · cited by 1
- Multiset.left_notMem_Ioostatement · cited by 1
- Multiset.mem_Ioostatement · cited by 1
- Multiset.Ioo_eq_zerostatement and proof · cited by 1
- Multiset.card_Ioo_eq_card_Icc_sub_twostatement · cited by 0
- Multiset.card_Ioo_eq_card_Ico_sub_onestatement · cited by 0
- Multiset.right_notMem_Ioostatement · cited by 0
- Multiset.map_add_right_Ioostatement and proof · cited by 0
- Multiset.nodup_Ioostatement · cited by 0
- Multiset.Ioo_cons_leftstatement · cited by 0
- Multiset.Ioo_eq_zero_iffstatement · cited by 0
- Multiset.Ioo_eq_zero_of_lestatement · cited by 0