Theorems · Theorem · order theory
Directed.finset_le
∀ {α : Type u} {r : α → α → Prop} [IsTrans α r] {ι : Type u_1} [hι : Nonempty ι] {f : ι → α},
Directed r f → ∀ (s : Finset ι), ∃ z, ∀ i ∈ s, r (f i) (f z)- Defined in
- Mathlib.Data.Finset.Order
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Multisetproof · cited by 2,627
- Finset.valproof · cited by 438
- Multiset.consproof · cited by 313
- Directedstatement and proof · cited by 213
- IsTransstatement and proof · cited by 157
- transproof · cited by 111
- Multiset.induction_onproof · cited by 109
- Multiset.mem_consproof · cited by 29
Cited by6
Results whose statement or proof uses this declaration.
- Directed.measure_iUnionproof · cited by 5
- Finset.exists_leproof · cited by 4
- linearIndepOn_iUnion_of_directedproof · cited by 4
- Directed.finite_set_leproof · cited by 3
- sSupIndep_iUnion_of_directedproof · cited by 1
- algebraicIndependent_iUnion_of_directedproof · cited by 1