Theorems · Theorem · order theory
Finset.Ioo_eq_empty_iff
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] [DenselyOrdered α],
Finset.Ioo a b = ∅ ↔ ¬a < b- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- DenselyOrderedstatement and proof · cited by 471
- Finset.Ioostatement · cited by 185
- Finset.coe_Iooproof · cited by 48
- Finset.coe_eq_emptyproof · cited by 8
- Set.Ioo_eq_empty_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.Ioo_eq_zero_iffproof · cited by 0