Theorems · Theorem · order theory
Set.nonempty_Ioi
∀ {α : Type u_1} [inst : Preorder α] {a : α} [NoMaxOrder α], (Set.Ioi a).Nonempty- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- PreorderNoMaxOrder
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.
- Preorderstatement and proof · cited by 7,952
- Set.Nonemptystatement · cited by 2,627
- Set.Ioistatement · cited by 1,463
- NoMaxOrderstatement and proof · cited by 340
- NoMaxOrder.exists_gtproof · cited by 62
Cited by10
Results whose statement or proof uses this declaration.
- closure_Ioiproof · cited by 11
- interior_Iicproof · cited by 6
- frontier_Iicproof · cited by 3
- csInf_Ioiproof · cited by 3
- isConnected_Ioiproof · cited by 2
- frontier_Ioiproof · cited by 2
- Order.succ_eq_csInfproof · cited by 1
- MeasureTheory.Measure.measure_Ioi_posproof · cited by 0
- not_bddAbove_Ioiproof · cited by 0
- nhdsWithin_Ioi_neBotproof · cited by 0