Theorems · Theorem · order theory
UpperSet.Ioi_eq_top
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, UpperSet.Ioi a = ⊤ ↔ a = ⊤- Defined in
- Mathlib.Order.UpperLower.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderOrderTop
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.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- UpperSetstatement · cited by 245
- UpperSet.Ioistatement · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mem_ballAddSubgroup_iffproof · cited by 0