Theorems · Theorem · order theory
Finset.sup_eq_iSup
∀ {α : Type u_2} {β : Type u_3} [inst : CompleteLattice β] (s : Finset α) (f : α → β), s.sup f = ⨆ a ∈ s, f a- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- Finset.supstatement · cited by 530
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- Finset.le_supproof · cited by 112
- le_iSup_of_leproof · cited by 79
- Finset.sup_leproof · cited by 44
Cited by30
Results whose statement or proof uses this declaration.
- Finset.sup_set_eq_biUnionproof · cited by 15
- Finset.sup_id_eq_sSupproof · cited by 12
- Submodule.supIndep_torsionBySet_idealproof · cited by 4
- Module.End.independent_genEigenspaceproof · cited by 4
- MeasureTheory.Content.innerContent_iSup_natproof · cited by 3
- iSupIndep_comp_coe_iff_supIndepproof · cited by 3
- iSup_fin_threeproof · cited by 3
- Finset.sup_univ_eq_iSupproof · cited by 3
- iSupIndep_iff_supIndep_univproof · cited by 2
- Finset.wellFoundedOn_bUnionproof · cited by 1
- disjointed_eq_inf_complproof · cited by 1
- Submodule.fg_iff_compactproof · cited by 1