Theorems · Theorem · order theory
Set.compl_Iic
∀ {α : Type u_1} [inst : LinearOrder α] {a : α}, (Set.Iic a)ᶜ = Set.Ioi a- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 10 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_leproof · cited by 328
Cited by10
Results whose statement or proof uses this declaration.
- isOpen_Ioiproof · cited by 43
- interior_Ici'proof · cited by 13
- borel_eq_generateFrom_Iicproof · cited by 4
- surjOn_Ioi_of_monotone_surjectiveproof · cited by 2
- eventually_le_const_iff_forall_gt_eventually_lt_constproof · cited by 2
- lowerSemicontinuous_iff_isClosed_preimageproof · cited by 1
- Set.Iic_sdiff_Iicproof · cited by 1
- ProbabilityTheory.lintegral_betaPDFproof · cited by 1
- Real.borel_eq_generateFrom_Iic_ratproof · cited by 1
- Set.Iio_sdiff_Iicproof · cited by 0