Theorems · Theorem · order theory
Finset.sup_set_eq_biUnion
∀ {α : Type u_2} {β : Type u_3} (s : Finset α) (f : α → Set β), s.sup f = ⋃ x ∈ s, f x- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 60 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
- Finsetstatement and proof · cited by 13,712
- Set.iUnionstatement · cited by 2,483
- Finset.supstatement · cited by 530
- Finset.sup_eq_iSupproof · cited by 30
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_leproof · cited by 3
- Finset.apply_union_le_sumproof · cited by 2
- MeasureTheory.VectorMeasure.le_variationproof · cited by 1
- Set.partialSups_eq_accumulateproof · cited by 1
- MeasureTheory.AddContent.supClosure_apply_finpartitionproof · cited by 1
- TopologicalSpace.NoetherianSpace.exists_finite_set_isClosed_irreducibleproof · cited by 1
- MeasureTheory.preVariation.sum_le_preVariationFun_iUnion'proof · cited by 1
- MeasureTheory.VectorMeasure.sum_finpartitionproof · cited by 1
- MeasureTheory.IsSetRing.finsetSup_memproof · cited by 1
- biUnion_Ioc_disjointed_of_monotoneproof · cited by 1
- Set.definable_biUnion_finsetproof · cited by 0
- Set.definable_iUnion_of_finiteproof · cited by 0