Theorems · Theorem · order theory
Set.inter_compl_self
∀ {α : Type u_1} (s : Set α), s ∩ sᶜ = ∅- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- inf_compl_eq_botproof · cited by 4
Cited by17
Results whose statement or proof uses this declaration.
- Filter.compl_notMemproof · cited by 6
- MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrictproof · cited by 6
- MeasureTheory.condExp_indicatorproof · cited by 5
- IsLocallyConstant.apply_eq_of_isPreconnectedproof · cited by 5
- Filter.mem_iff_inf_principal_complproof · cited by 4
- Ergodic.of_mem_extremePoints_measure_univ_eqproof · cited by 2
- MeasureTheory.addContent_iUnion_eq_sum_of_tendsto_zeroproof · cited by 2
- Set.image_compl_subsetproof · cited by 2
- boundary_principalproof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- Set.union_inter_compl_left_subsetproof · cited by 1
- Set.union_inter_compl_right_subsetproof · cited by 1