Theorems · Theorem · order theory
Set.union_compl_self
∀ {α : Type u_1} (s : Set α), s ∪ sᶜ = Set.univ- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.univstatement · cited by 3,945
- Compl.complstatement · cited by 2,925
- emproof · cited by 115
- Set.eq_univ_iff_forallproof · cited by 93
Cited by57
Results whose statement or proof uses this declaration.
- Set.ncard_add_ncard_complproof · cited by 16
- Set.compl_union_selfproof · cited by 13
- measurable_of_restrict_of_restrict_complproof · cited by 9
- MeasureTheory.Measure.restrict_add_restrict_complproof · cited by 8
- ProbabilityTheory.Kernel.rnDeriv_add_singularPartproof · cited by 7
- isClopen_iffproof · cited by 6
- IsLocallyConstant.apply_eq_of_isPreconnectedproof · cited by 5
- IsPreconnected.subset_isClopenproof · cited by 4
- MeasureTheory.Measure.MutuallySingular.self_iffproof · cited by 4
- MeasureTheory.integral_add_compl₀proof · cited by 4
- MeasureTheory.average_mem_openSegment_compl_selfproof · cited by 4
- Set.indicator_const_preimage_eq_unionproof · cited by 3