Theorems · Theorem
Set.mem_iUnion
∀ {α : Type u} {ι : Sort v} {x : α} {s : ι → Set α}, x ∈ ⋃ i, s i ↔ ∃ i, x ∈ s i- Defined in
- Mathlib.Order.SetNotation
- Cited by
- 212 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 22 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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 and proof · cited by 2,483
Cited by212
Results whose statement or proof uses this declaration.
- Set.ofPred_existsproof · cited by 23
- Set.mem_iUnion_of_memproof · cited by 23
- MeasureTheory.lintegral_eq_zero_iff'proof · cited by 16
- MeasureTheory.lintegral_iSupproof · cited by 16
- IsLindelof.elim_countable_subcoverproof · cited by 10
- Submodule.mem_iSup_of_directedproof · cited by 7
- IsCompact.add_closedBall_zeroproof · cited by 5
- MeasureTheory.Measure.hausdorffMeasure_zero_singletonproof · cited by 5
- isCompact_of_finite_subcoverproof · cited by 5
- AddSubmonoid.iSup_inductionproof · cited by 5
- IsCoveringMap.exists_path_liftsproof · cited by 4
- Subalgebra.coe_iSup_of_directedproof · cited by 4
Showing the 200 most cited of 212.