Theorems · Theorem · order theory
Finset.exists_le
∀ {α : Type u} [Nonempty α] [inst : Preorder α] [IsDirectedOrder α] (s : Finset α), ∃ M, ∀ i ∈ s, i ≤ M- Defined in
- Mathlib.Data.Finset.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Preorderstatement and proof · cited by 7,952
- IsDirectedOrderstatement and proof · cited by 316
- directed_idproof · cited by 7
- Directed.finset_leproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.exists_forall_leproof · cited by 2
- Asymptotics.bound_of_isBigO_cofiniteproof · cited by 2
- Filter.tendsto_finset_Iic_atTop_atTopproof · cited by 2
- FirstOrder.Language.age_directLimitproof · cited by 1