Theorems · Theorem · order theory
Set.iUnion_iUnion_eq_or_left
∀ {α : Type u_1} {β : Type u_2} {b : β} {p : β → Prop} {s : (x : β) → x = b ∨ p x → Set α},
⋃ x, ⋃ (h : x = b ∨ p x), s x h = s b ⋯ ∪ ⋃ x, ⋃ (h : p x), s x ⋯- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.iUnion_iUnion_eq_leftproof · cited by 27
- Set.iUnion_union_distribproof · cited by 4
- Set.iUnion_orproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- Set.biUnion_insertproof · cited by 13
- AlgebraicGeometry.Scheme.zeroLocus_biInfproof · cited by 2
- asymptoticCone_biUnionproof · cited by 2
- PrimitiveSpectrum.hull_finsetInfproof · cited by 2
- BoxIntegral.Prepartition.iUnion_splitproof · cited by 1
- MeasureTheory.VectorMeasure.IntegrableOn.biUnion_finiteproof · cited by 1
- MeasureTheory.measureReal_biUnion_finset_leproof · cited by 1
- MeasureTheory.OuterMeasure.IsCaratheodory.biUnion_of_finiteproof · cited by 1
- Ioc_subset_biUnion_Iocproof · cited by 1
- Set.biUnion_pairproof · cited by 1
- Finset.isCountablyCompact_biUnionproof · cited by 1
- MeasureTheory.integrableOn_finite_biUnionproof · cited by 1