Theorems · Theorem · order theory
Set.compl_Ioi
∀ {α : Type u_1} [inst : LinearOrder α] {a : α}, (Set.Ioi a)ᶜ = Set.Iic a- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 7 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.Ioistatement · cited by 1,463
- Set.Iicstatement · cited by 1,111
- not_ltproof · cited by 306
Cited by7
Results whose statement or proof uses this declaration.
- borel_eq_generateFrom_Iicproof · cited by 4
- Set.Ioi_sdiff_Ioiproof · cited by 2
- Set.Ici_sdiff_Ioiproof · cited by 1
- Order.IsNormal.continuousproof · cited by 1
- Real.borel_eq_generateFrom_Iic_ratproof · cited by 1
- integral_gaussian_complex_Ioiproof · cited by 1
- IsUpperSet.eq_univ_or_Ioiproof · cited by 0