Theorems · Theorem · order theory
Set.biUnion_empty
∀ {α : Type u_1} {β : Type u_2} (s : α → Set β), ⋃ x ∈ ∅, s x = ∅- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 12 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.iUnionstatement · cited by 2,483
- iSup_emptysetproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Ideal.subset_union_primeproof · cited by 4
- AddSubgroup.exists_finiteIndex_of_leftCoset_coverproof · cited by 2
- IsCompact.cthickening_eq_biUnion_closedBallproof · cited by 2
- Ideal.subset_union_prime'proof · cited by 1
- AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- Subgroup.exists_finiteIndex_of_leftCoset_coverproof · cited by 1
- Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- Metric.cthickening_eq_biUnion_closedBallproof · cited by 1
- Set.Finite.bddAbove_biUnionproof · cited by 0
- Set.Finite.bddBelow_biUnionproof · cited by 0
- Monotone.biUnion_Ico_Ioc_map_succproof · cited by 0
- Geometry.SimplicialComplex.space_botproof · cited by 0