DirectedOn.exists_mem_subset_of_finite_of_subset_sUnion

∀ {α : Type u_1} {c : Set (Set α)},
  c.Nonempty → DirectedOn (fun x1 x2 => x1 ⊆ x2) c → ∀ {s : Set α}, s.Finite → s ⊆ ⋃₀ c → ∃ t ∈ c, s ⊆ t

Defined in: Mathlib.Data.Set.Finite.Lattice
Cited by: 2 results in Mathlib
Foundations: Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

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