Theorems · Theorem · order theory
Set.compl_sUnion
∀ {α : Type u_1} (S : Set (Set α)), (⋃₀ S)ᶜ = ⋂₀ (compl '' S)- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- Compl.complstatement and proof · cited by 2,925
- Set.extproof · cited by 2,266
- Set.sUnionstatement and proof · cited by 392
- Set.sInterstatement · cited by 225
- Set.sInter_imageproof · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- closure_eq_compl_interior_complproof · cited by 7
- Set.sUnion_eq_compl_sInter_complproof · cited by 3
- DirSupInaccOn.sUnionproof · cited by 2
- regularSpace_generateFromproof · cited by 0
- MeasureTheory.Measure.support_eq_sInterproof · cited by 0
- compactSpace_generateFrom_of_compl_memproof · cited by 0