Theorems · Theorem · order theory
Set.compl_Ici
∀ {α : Type u_1} [inst : LinearOrder α] {a : α}, (Set.Ici a)ᶜ = Set.Iio a- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 11 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_leproof · cited by 328
Cited by11
Results whose statement or proof uses this declaration.
- isOpen_Iioproof · cited by 38
- Nat.cofinite_eq_atTopproof · cited by 37
- Topology.IsLower.isTopologicalBasis_insert_univ_subbasisproof · cited by 2
- ProbabilityTheory.lintegral_gammaPDF_eq_oneproof · cited by 2
- upperSemicontinuous_iff_isClosed_preimageproof · cited by 1
- ProbabilityTheory.lintegral_paretoPDF_eq_oneproof · cited by 1
- Set.Ici_sdiff_Iciproof · cited by 1
- ProbabilityTheory.lintegral_betaPDFproof · cited by 1
- Set.Ioi_sdiff_Iciproof · cited by 1
- Topology.IsLower.isTopologicalSpace_basisproof · cited by 1
- Real.borel_eq_generateFrom_Ici_ratproof · cited by 0