rw [Set.disjoint_iff_inter_eq_empty.mp huv, Set.inter_empty]
α : Type u_1
inst✝ : TopologicalSpace α
s u v : Set α
hu : IsClosed u
hv : IsClosed v
huv : Disjoint u v
hsuv : s ⊆ u ∪ v
hs : IsPreconnected s
⊢ s ∩ (u ∩ v) = ∅
no goals