Theorems · Theorem · combinatorics
Finset.mem_biUnion
∀ {α : Type u_1} {β : Type u_2} {s : Finset α} {t : α → Finset β} [inst : DecidableEq β] {b : β},
b ∈ s.biUnion t ↔ ∃ a ∈ s, b ∈ t a- Defined in
- Mathlib.Data.Finset.Union
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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.
- Finsetstatement and proof · cited by 13,712
- Finset.valproof · cited by 438
- Finset.biUnionstatement · cited by 217
Cited by26
Results whose statement or proof uses this declaration.
- Finset.sup_eq_biUnionproof · cited by 7
- ProbabilityTheory.IsGaussianProcess.of_isGaussianProcessproof · cited by 4
- Finset.SupIndep.biUnionproof · cited by 4
- Finset.sum_comm'proof · cited by 2
- Configuration.Nondegenerate.exists_injective_of_card_leproof · cited by 2
- Finset.addEnergy_eq_sum_sq'proof · cited by 2
- PairReduction.iSup_edist_pairSetproof · cited by 1
- ax_grothendieck_of_locally_finiteproof · cited by 1
- Finpartition.mem_bindproof · cited by 1
- BoxIntegral.Prepartition.eventually_not_disjoint_imp_le_of_mem_splitManyproof · cited by 1
- Finset.iInf_biUnionproof · cited by 1
- Finset.all_card_le_biUnion_card_iff_existsInjective'proof · cited by 1