Theorems · Theorem · order theory
Set.compl_union_self
∀ {α : Type u_1} (s : Set α), sᶜ ∪ s = Set.univ- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 24 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 and proof · cited by 3,945
- Compl.complstatement and proof · cited by 2,925
- Set.union_commproof · cited by 99
- Set.union_compl_selfproof · cited by 57
Cited by13
Results whose statement or proof uses this declaration.
- nhdsNE_sup_pureproof · cited by 4
- MeasureTheory.FinStronglyMeasurable.exists_set_sigmaFiniteproof · cited by 3
- MeasureTheory.sigmaFinite_restrict_sigmaFiniteSetWRT'proof · cited by 3
- MeasureTheory.integrable_iff_integrableAtFilter_cocompactproof · cited by 3
- precise_refinement_setproof · cited by 3
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- eventuallyEq_insertproof · cited by 2
- PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopenproof · cited by 2
- SSet.subcomplex_le_horn_iffproof · cited by 2
- Set.infinite_of_finite_complproof · cited by 2
- Measurable.measurable_of_countable_neproof · cited by 1
- Real.continuousAt_rpow_of_posproof · cited by 1