Theorems · Theorem · order theory
Multiset.Ioo_eq_zero
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] {a b : α}, ¬a < b → Multiset.Ioo a b = 0- Defined in
- Mathlib.Order.Interval.Multiset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderLocallyFiniteOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LT.lt.transproof · cited by 370
- Multiset.Ioostatement and proof · cited by 13
- Multiset.eq_zero_iff_forall_notMemproof · cited by 7
- Multiset.mem_Iooproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.Ioo_eq_zero_of_leproof · cited by 0