Theorems · Theorem · order theory
Finset.le_sup
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s : Finset β} {f : β → α} {b : β},
b ∈ s → f b ≤ s.sup f- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 55 from the axioms, rests on 845 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSupOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- le_rflproof · cited by 1,558
- 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 by112
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_lt_iffproof · cited by 23
- Finpartition.leproof · cited by 15
- MonomialOrder.le_degreeproof · cited by 11
- Polynomial.le_degree_of_ne_zeroproof · cited by 11
- Finset.sup_mono_funproof · cited by 7
- Finset.le_sup_of_leproof · cited by 7
- SimpleGraph.card_edgeFinset_le_extremalNumberproof · cited by 6
- MvPolynomial.le_totalDegreeproof · cited by 6
- AddMonoidAlgebra.sup_support_coeff_mul_leproof · cited by 5