Theorems · Theorem · order theory
Set.biUnion_insert
∀ {α : Type u_1} {β : Type u_2} (a : α) (s : Set α) (t : α → Set β), ⋃ x ∈ insert a s, t x = t a ∪ ⋃ x ∈ s, t x- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 13 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.
Cites4
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_congr_Propproof · cited by 374
- Set.iUnion_iUnion_eq_or_leftproof · cited by 18
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.IsSetRing.biUnion_memproof · cited by 5
- Ideal.subset_union_primeproof · cited by 4
- IsPreconnected.biUnion_of_reflTransGenproof · cited by 3
- Metric.AreSeparated.finite_iUnion_left_iffproof · cited by 3
- nhdsWithin_biUnionproof · cited by 2
- MeasureTheory.addContent_biUnion_leproof · cited by 2
- Ideal.subset_union_prime'proof · cited by 1
- Topology.IsConstructible.induction_of_isTopologicalBasisproof · cited by 1
- StieltjesFunction.length_subadditive_Icc_Iooproof · 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