Theorems · Theorem · order theory
Set.Ioi_eq_singleton_iff
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, Set.Ioi a = {b} ↔ IsTop b ∧ a ⋖ b- Defined in
- Mathlib.Order.Cover
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Set.Ioistatement and proof · cited by 1,463
- LT.lt.neproof · cited by 872
- OrderTopproof · cited by 493
- LT.lt.transproof · cited by 370
- not_ltproof · cited by 306
- CovBystatement and proof · cited by 290
- IsTopstatement and proof · cited by 77
- isTop_topproof · cited by 10
- Set.Ioc_topproof · cited by 4
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