Theorems · Theorem · order theory
Multiset.Ico_eq_zero_iff
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] {a b : α}, Multiset.Ico a b = 0 ↔ ¬a < b- Defined in
- Mathlib.Order.Interval.Multiset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 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.
Cites6
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 and proof · cited by 2,627
- LocallyFiniteOrderstatement and proof · cited by 658
- Multiset.Icostatement · cited by 32
- Finset.val_eq_zeroproof · cited by 12
- Finset.Ico_eq_empty_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.Ico_eq_zeroproof · cited by 1