Theorems · Theorem · order theory
Set.nonempty_iUnion
∀ {α : Type u_1} {ι : Sort u_5} {s : ι → Set α}, (⋃ i, s i).Nonempty ↔ ∃ i, (s i).Nonempty- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 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.Nonemptystatement · cited by 2,627
- Set.iUnionstatement · cited by 2,483
Cited by6
Results whose statement or proof uses this declaration.
- AddAction.isTopologicallyTransitive_iff_dense_iUnion_preimageproof · cited by 2
- TopologicalSpace.IsOpenCover.jacobsonSpace_iffproof · cited by 1
- IsConnected.iUnion_of_reflTransGenproof · cited by 1
- AddAction.isTopologicallyTransitive_iff_dense_iUnionproof · cited by 1
- AddAction.isTopologicallyTransitive_iff_dense_of_preimage_invariantproof · cited by 0
- MulAction.isTopologicallyTransitive_iff_dense_of_preimage_invariantproof · cited by 0