Theorems · Theorem · order theory
Set.compl_Iio
∀ {α : Type u_1} [inst : LinearOrder α] {a : α}, (Set.Iio a)ᶜ = Set.Ici a- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 17 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
- Compl.complstatement · cited by 2,925
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- Set.Icistatement · cited by 1,070
- not_ltproof · cited by 306
Cited by8
Results whose statement or proof uses this declaration.
- interior_Ici'proof · cited by 13
- borel_eq_generateFrom_Iioproof · cited by 6
- IsLowerSet.eq_univ_or_Iioproof · cited by 2
- eventually_le_const_iff_forall_gt_eventually_lt_constproof · cited by 2
- MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasureproof · cited by 1
- Set.Iio_sdiff_Iioproof · cited by 0
- Set.Iic_sdiff_Iioproof · cited by 0
- Real.borel_eq_generateFrom_Ici_ratproof · cited by 0