Theorems · Theorem · order theory
Finset.le_sup_of_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 : β}, b ∈ s → a ≤ f b → a ≤ s.sup f- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 56 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
- LE.le.transproof · cited by 3,151
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- Finset.le_supproof · cited by 112
Cited by7
Results whose statement or proof uses this declaration.
- MvPolynomial.le_degrees_add_leftproof · cited by 2
- SchwartzMap.one_add_le_sup_seminorm_applyproof · cited by 1
- MvPolynomial.aeval_natDegree_leproof · cited by 1
- Filter.tendsto_finset_powerset_atTop_atTopproof · cited by 1
- LocallyLipschitzOn.exists_lipschitzOnWith_of_compactproof · cited by 1
- Isometry.singleproof · cited by 1
- SimpleGraph.two_mul_extremalNumber_le_zarankiewicz_symmproof · cited by 0