Theorems · Theorem · order theory
Set.Ioi_infinite
∀ {α : Type u_1} [inst : Preorder α] [NoMaxOrder α] (a : α), (Set.Ioi a).Infinite- Defined in
- Mathlib.Order.Interval.Set.Infinite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- 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.Ioistatement · cited by 1,463
- NoMaxOrderstatement and proof · cited by 340
- Set.Infinitestatement · cited by 263
- Set.infinite_coe_iffproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- infinite_not_isOfFinAddOrderproof · cited by 2
- infinite_not_isOfFinOrderproof · cited by 1
- Polynomial.existsUnique_hilbertPolyproof · cited by 1
- AddRightCancelMonoid.infinite_not_isOfFinAddOrderproof · cited by 0
- RightCancelMonoid.infinite_not_isOfFinOrderproof · cited by 0