Theorems · Theorem · order theory
Set.sUnion_eq_biUnion
∀ {α : Type u_1} {s : Set (Set α)}, ⋃₀ s = ⋃ i ∈ s, i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 51 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.
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.iUnionstatement · cited by 2,483
- Set.sUnionstatement and proof · cited by 392
- Set.image_id'proof · cited by 86
- Set.sUnion_imageproof · cited by 28
Cited by51
Results whose statement or proof uses this declaration.
- IsSemilinearSet.imageproof · cited by 9
- MeasurableSet.sUnionproof · cited by 5
- TopologicalSpace.Opens.isBasis_iff_coverproof · cited by 4
- Set.preimage_sUnionproof · cited by 2
- DirectedOn.exists_mem_subset_of_finite_of_subset_sUnionproof · cited by 2
- sSup_sUnionproof · cited by 2
- TopologicalSpace.IsTopologicalBasis.compactsproof · cited by 2
- Set.sUnion_iUnionproof · cited by 2
- closure_sUnion_irreducibleComponents_sdiff_singletonproof · cited by 2
- MeasureTheory.measure_sUnionproof · cited by 1
- MeasureTheory.measure_sUnion_null_iffproof · cited by 1
- MeasurableSpace.measurableSet_generateFrom_memPartition_iffproof · cited by 1