Theorems · Theorem · order theory
Finset.sup_le
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s : Finset β} {f : β → α} {a : α},
(∀ b ∈ s, f b ≤ a) → s.sup f ≤ aAlias of the reverse direction of Finset.sup_le_iff.
- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, 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
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- Finset.sup_le_iffproof · cited by 25
Cited by44
Results whose statement or proof uses this declaration.
- Finset.sup'_eq_supproof · cited by 35
- Finset.sup_eq_iSupproof · cited by 30
- Finset.sup_monoproof · cited by 25
- Finset.sup_mono_funproof · cited by 7
- Finset.sup_Iicproof · cited by 4
- Polynomial.trinomial_natDegreeproof · cited by 4
- sup_eq_of_isMaxOnproof · cited by 3
- MvPolynomial.IsHomogeneous.totalDegree_leproof · cited by 3
- Polynomial.degree_derivativeproof · cited by 3
- Multiset.finsetSum_eq_sup_iff_disjointproof · cited by 2
- Matrix.linfty_opNNNorm_eq_opNNNormproof · cited by 2
- MvPolynomial.le_degrees_add_leftproof · cited by 2