Theorems · Theorem · order theory
Set.Ioc_infinite
∀ {α : Type u_1} [inst : Preorder α] [DenselyOrdered α] {a b : α}, a < b → (Set.Ioc a b).Infinite- Defined in
- Mathlib.Order.Interval.Set.Infinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Iocstatement · cited by 971
- DenselyOrderedstatement and proof · cited by 471
- Set.Infinitestatement · cited by 263
- Set.Ioo_subset_Ioc_selfproof · cited by 30
- Set.Infinite.monoproof · cited by 25
- Set.Ioo_infiniteproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Set.Ioc.infiniteproof · cited by 0