Theorems · Theorem · order theory
Set.sUnion_empty
∀ {α : Type u_1}, ⋃₀ ∅ = ∅- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 17 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 · cited by 53,352
- Set.sUnionstatement · cited by 392
- sSup_emptyproof · cited by 19
Cited by17
Results whose statement or proof uses this declaration.
- isOpen_emptyproof · cited by 23
- Ultrafilter.finite_sUnion_mem_iffproof · cited by 5
- TopologicalSpace.vietoris.isTopologicalBasisproof · cited by 2
- IsGδ.sUnionproof · cited by 2
- IsSemilinearSet.sUnionproof · cited by 2
- MeasurableSpace.measurableSet_generateFrom_memPartition_iffproof · cited by 1
- IsProperSemilinearSet.sUnionproof · cited by 1
- Convexity.IsConvexSet.sUnionproof · cited by 1
- IsSemilinearSet.emptyproof · cited by 1
- TopologicalSpace.IsTopologicalBasis.nonemptyCompactsproof · cited by 1
- isConnected_iff_sUnion_disjoint_openproof · cited by 0
- IsProperSemilinearSet.emptyproof · cited by 0