Theorems · Theorem · order theory
Set.mem_compl
∀ {α : Type u_1} {s : Set α} {x : α}, x ∉ s → x ∈ sᶜ- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Compl.complstatement · cited by 2,925
Cited by18
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMapproof · cited by 23
- IsClosed.compl_mem_nhdsproof · cited by 9
- IsDedekindDomain.HeightOneSpectrum.valuation_of_mk'proof · cited by 4
- IsOrderBornology.atTop_le_coboundedproof · cited by 4
- LightProfinite.epi_iff_surjectiveproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.valuation_defstatement and proof · cited by 3
- Profinite.epi_iff_surjectiveproof · cited by 2
- Set.indicator_add_compl_eq_piecewiseproof · cited by 2
- MulAction.IsPretransitive.of_partitionproof · cited by 1
- OnePoint.nhdsNE_infty_eqproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eqproof · cited by 1
- ProfiniteGrp.closedSubgroup_eq_sInf_openproof · cited by 0