Theorems · Theorem · order theory
Set.Ioc_top
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : OrderTop α] {a : α}, Set.Ioc a ⊤ = Set.Ioi a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topstatement · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- Set.Ioistatement and proof · cited by 1,463
- Set.Iocstatement · cited by 971
- OrderTopstatement and proof · cited by 493
- Set.inter_univproof · cited by 198
- Set.Iic_topproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- nhds_top_basisproof · cited by 5
- Continuous.strictMono_of_inj_boundedOrderproof · cited by 3
- Set.Ioi_eq_singleton_iffproof · cited by 0
- unitInterval.subtype_Ioi_eq_Iocproof · cited by 0