apply (isPreconnected_iff_subset_of_disjoint_closed.mp hs) u v hu hv hsuv
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 ∨ s ⊆ v
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) = ∅