Theorems · Theorem · order theory
Set.Iio_union_Ioi_of_lt
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, a < b → Set.Iio b ∪ Set.Ioi a = Set.univ- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
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.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.univstatement · cited by 3,945
- Set.Ioistatement · cited by 1,463
- Set.Iiostatement · cited by 1,166
- Set.eq_univ_of_forallproof · cited by 80
- LT.lt.gt_or_ltproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- denselyOrdered_of_preconnectedSpaceproof · cited by 0