Theorems · Theorem · order theory
Finset.nonempty_Ioc
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], (Finset.Ioc a b).Nonempty ↔ 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
- Assumes
- PreorderLocallyFiniteOrder
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
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptyproof · cited by 2,627
- Finset.Nonemptystatement · cited by 1,001
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iocstatement · cited by 301
- Finset.coe_Iocproof · cited by 55
- Finset.coe_nonemptyproof · cited by 18
- Set.nonempty_Iocproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Finset.Aesop.nonempty_Ioc_of_ltproof · cited by 0