Theorems · Theorem · order theory
Set.sUnion_insert
∀ {α : Type u_1} (s : Set α) (T : Set (Set α)), ⋃₀ insert s T = s ∪ ⋃₀ T- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 60 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
- Set.sUnionstatement · cited by 392
- sSup_insertproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- Ultrafilter.finite_sUnion_mem_iffproof · cited by 5
- TopologicalSpace.vietoris.isTopologicalBasisproof · cited by 2
- MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRingproof · cited by 2
- IsGδ.sUnionproof · cited by 2
- IsSemilinearSet.sUnionproof · cited by 2
- MeasureTheory.IsSetSemiring.sUnion_insert_disjointOfDiffproof · cited by 1
- IsProperSemilinearSet.sUnionproof · cited by 1
- isStationary_union_iffproof · cited by 0
- MeasureTheory.IsSetSemiring.Iocproof · cited by 0
- isConnected_iff_sUnion_disjoint_openproof · cited by 0
- IsSemilinearSet.closureproof · cited by 0