Theorems · Theorem · order theory
Set.Ioi_eq_empty_iff
∀ {α : Type u_1} [inst : Preorder α] {a : α}, Set.Ioi a = ∅ ↔ IsMax a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Ioistatement · cited by 1,463
- IsMaxstatement · cited by 372
- Set.mem_Ioiproof · cited by 80
- Set.eq_empty_iff_forall_notMemproof · cited by 42
- isMax_iff_forall_not_ltproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsMax.Ioi_eqproof · cited by 6
- Finset.Ioi_eq_emptyproof · cited by 4
- Set.Ioi_nonemptyproof · cited by 0