no goals
α : Type u
β : Type v
γ : Type w
inst✝² : TopologicalSpace α
inst✝¹ : LinearOrder α
inst✝ : OrderTopology α
a : α
s : Set α
hs : s ∈ 𝓝 a
u : α
hu : a < u
⊢ ∃ u', u' ∈ Ioc a u ∧ Ico a u' ⊆ s
simpa only [OrderDual.exists, exists_prop, dual_Ico, dual_Ioc] using
  exists_Ioc_subset_of_mem_nhds' (show ofDual ⁻¹' s ∈ 𝓝 (toDual a) from hs) hu.dual