Theorems · Theorem · combinatorics
Finset.disjiUnion_eq_biUnion
∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] (s : Finset α) (f : α → Finset β) (hf : (↑s).PairwiseDisjoint f),
s.disjiUnion f hf = s.biUnion f- Defined in
- Mathlib.Data.Finset.Union
- Cited by
- 11 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.
Cites8
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
- SetLike.coestatement and proof · cited by 8,199
- Set.PairwiseDisjointstatement and proof · cited by 275
- Finset.biUnionstatement · cited by 217
- Finset.eq_of_veqproof · cited by 45
- Finset.nodupproof · cited by 40
- Finset.disjiUnionstatement and proof · cited by 37
- Multiset.Nodup.dedupproof · cited by 15
Cited by11
Results whose statement or proof uses this declaration.
- Finset.sum_biUnionproof · cited by 10
- Finset.prod_biUnionproof · cited by 3
- Finset.addEnergy_eq_sum_sq'proof · cited by 2
- Finset.mulEnergy_eq_sum_sq'proof · cited by 2
- Finset.disjiUnion_Iic_disjointedproof · cited by 2
- SimpleGraph.coe_finsetWalkLengthLT_eqproof · cited by 1
- List.fixedLengthDigits_succ_eq_disjiUnionproof · cited by 1
- SimpleGraph.disjiUnion_supp_toFinset_eq_supp_toFinsetproof · cited by 1
- Finset.powerset_card_biUnionproof · cited by 0
- SimpleGraph.CompleteEquipartiteSubgraph.verts_eq_biUnionproof · cited by 0
- Finset.piAntidiag_insertproof · cited by 0