Theorems · Theorem · order theory
Finset.sup_insert
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s : Finset β} {f : β → α}
[inst_2 : DecidableEq β] {b : β}, (insert b s).sup f = f b ⊔ s.sup f- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 58 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.
- Finsetstatement and proof · cited by 13,712
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- Finset.fold_insert_idemproof · cited by 5
Cited by35
Results whose statement or proof uses this declaration.
- Module.End.independent_genEigenspaceproof · cited by 4
- Finset.sup_eq_bot_iffproof · cited by 4
- MeasureTheory.IsSetSemiring.isSetRing_supClosureproof · cited by 3
- disjointedRecproof · cited by 3
- Multiset.count_finset_supproof · cited by 3
- MeasureTheory.Content.innerContent_iSup_natproof · cited by 3
- iSup_fin_threeproof · cited by 3
- MeasureTheory.IsSetSemiring.mem_supClosure_iffproof · cited by 2
- MeasureTheory.SimpleFunc.finset_sup_applyproof · cited by 2
- Polynomial.degree_sum_eq_of_disjointproof · cited by 2
- Finset.sup_le_of_le_directedproof · cited by 2
- CompleteLattice.WellFoundedGT.isSupFiniteCompactproof · cited by 2