Theorems · Theorem · order theory
IsMax.Ioi_eq
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsMax a → Set.Ioi a = ∅Alias of the reverse direction of Set.Ioi_eq_empty_iff.
- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 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.
Cites5
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.Ioi_eq_empty_iffproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- SuccOrder.nhdsGTproof · cited by 5
- nhds_top_orderproof · cited by 4
- Set.Ioi_topproof · cited by 1
- nhdsGT_eq_bot_iffproof · cited by 1
- MeasureTheory.Filtration.rightCont_eq_of_isMaxproof · cited by 0
- Set.Ioi_Trueproof · cited by 0