Theorems · Theorem · order theory
Directed.finite_set_le
∀ {α : Type u_2} {r : α → α → Prop} [IsTrans α r] {γ : Type u_3} [Nonempty γ] {f : γ → α},
Directed r f → ∀ {s : Set γ}, s.Finite → ∃ z, ∀ i ∈ s, r (f i) (f z)- Defined in
- Mathlib.Data.Fintype.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Finitestatement and proof · cited by 1,814
- Set.Finite.toFinsetproof · cited by 351
- Directedstatement and proof · cited by 213
- IsTransstatement and proof · cited by 157
- Set.Finite.mem_toFinsetproof · cited by 74
- Directed.finset_leproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Directed.finite_leproof · cited by 5
- Set.Finite.exists_geproof · cited by 0
- Set.Finite.exists_leproof · cited by 0