no goals
α : Type u
β : Type v
γ : Type ?u.33531
δ : Type ?u.33534
ε : Type ?u.33537
ζ : Type ?u.33540
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace β
inst✝³ : TopologicalSpace γ
inst✝² : TopologicalSpace δ
inst✝¹ : TopologicalSpace ε
inst✝ : TopologicalSpace ζ
a : α
b : β
s : Set α
t : Set β
⊢ 𝓝[s ×ˢ t] (a, b) = 𝓝[s] a ×ˢ 𝓝[t] b
simp only [nhdsWithin, nhds_prod_eq, ← prod_inf_prod, prod_principal_principal]