Theorems · Theorem · order theory
Finset.sup_le_iff
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s : Finset β} {f : β → α} {a : α},
s.sup f ≤ a ↔ ∀ b ∈ s, f b ≤ a- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 54 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.
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
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- Finset.valproof · cited by 438
- Multiset.sup_leproof · cited by 3
Cited by25
Results whose statement or proof uses this declaration.
- Finset.le_supproof · cited by 112
- Finset.sup_leproof · cited by 44
- Finset.sup_image₂_leproof · cited by 5
- Finset.sup_constproof · cited by 5
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
- SimpleGraph.extremalNumber_of_fintypeCard_eqproof · cited by 3
- MvPolynomial.degreeOf_le_iffproof · cited by 2
- Finset.sup_erase_botproof · cited by 2
- edist_pi_le_iffproof · cited by 2
- Seminorm.finset_sup_le_sumproof · cited by 2
- Matrix.linfty_opNNNorm_eq_opNNNormproof · cited by 2
- CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSupproof · cited by 1