Theorems · Theorem · order theory
Finset.Ioi_eq_empty
∀ {α : Type u_2} {a : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrderTop α], Finset.Ioi a = ∅ ↔ IsMax a- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 4 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
- IsMaxstatement and proof · cited by 372
- LocallyFiniteOrderTopstatement and proof · cited by 114
- Finset.Ioistatement · cited by 106
- Finset.coe_Ioiproof · cited by 28
- Finset.coe_eq_emptyproof · cited by 8
- Set.Ioi_eq_empty_iffproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Finset.Iio_eq_emptyproof · cited by 3
- Finset.Ioi_topproof · cited by 0
- IsMax.finsetIoi_eqproof · cited by 0
- Finset.Ioi_nonemptyproof · cited by 0