Theorems · Definition · order theory
Finset.sup
{α : Type u_2} → {β : Type u_3} → [inst : SemilatticeSup α] → [OrderBot α] → Finset β → (β → α) → αSupremum of a finite set: sup {a, b, c} f = f a ⊔ f b ⊔ f c
- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 530 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 78 definitions · uses propext, Quot.sound
- Assumes
- SemilatticeSupOrderBot
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
- Bot.botproof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.foldproof · cited by 46
Cited by575
Results whose statement or proof uses this declaration.
- Finset.sup'proof · cited by 174
- MonomialOrder.degreeproof · cited by 132
- Finset.le_supstatement · cited by 112
- MvPolynomial.totalDegreeproof · cited by 76
- Finset.sup_emptystatement · cited by 72
- disjointedproof · cited by 64
- Finset.SupIndepproof · cited by 52
- MvPolynomial.degreesproof · cited by 51
- Finset.maxproof · cited by 50
- AddMonoidAlgebra.supDegreeproof · cited by 49
- Finset.sup_lestatement · cited by 44
- Finset.sup_singletonstatement · cited by 42
Showing the 200 most cited of 575.