Theorems · Theorem · order theory
Finset.sup_eq_biUnion
∀ {α : Type u_7} {β : Type u_8} [inst : DecidableEq β] (s : Finset α) (t : α → Finset β), s.sup t = s.biUnion t- Defined in
- Mathlib.Data.Finset.Lattice.Union
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 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.
Cites6
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.extproof · cited by 565
- Finset.supstatement · cited by 530
- Finset.biUnionstatement and proof · cited by 217
- Finset.mem_biUnionproof · cited by 26
- Finset.mem_supproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Finsupp.support_finsetSumproof · cited by 3
- Finpartition.biUnion_partsproof · cited by 3
- Finset.powersetCard_supproof · cited by 2
- Finset.disjiUnion_Iic_disjointedproof · cited by 2
- Finset.inclusion_exclusion_sum_inf_complproof · cited by 1
- Finset.powersetCard_biUnionproof · cited by 1
- Finset.SupIndep.supproof · cited by 0