Theorems · Theorem · order theory
Set.nonempty_Ioo_subtype
∀ {α : Type u_1} [inst : Preorder α] {a b : α} [DenselyOrdered α], a < b → Nonempty ↑(Set.Ioo a b)- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- PreorderDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Elemstatement · cited by 7,166
- Set.Ioostatement · cited by 1,214
- DenselyOrderedstatement and proof · cited by 471
- Set.Nonempty.to_subtypeproof · cited by 55
- Set.nonempty_Iooproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousOn.strictMonoOn_of_injOn_Iooproof · cited by 0