no goals
α : Type u
β : Type v
γ : Type ?u.45579
δ : Type ?u.45582
ε : Type ?u.45585
ζ : Type ?u.45588
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace β
inst✝³ : TopologicalSpace γ
inst✝² : TopologicalSpace δ
inst✝¹ : TopologicalSpace ε
inst✝ : TopologicalSpace ζ
t : Set α
ht : t ∈ fun s' => inst✝⁵.1 s'
⊢ IsOpen t ∧ IsOpen univ ∧ Prod.fst ⁻¹' t = t ×ˢ univ
simpa [Set.prod_eq] using ht
no goals
α : Type u
β : Type v
γ : Type ?u.45579
δ : Type ?u.45582
ε : Type ?u.45585
ζ : Type ?u.45588
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace β
inst✝³ : TopologicalSpace γ
inst✝² : TopologicalSpace δ
inst✝¹ : TopologicalSpace ε
inst✝ : TopologicalSpace ζ
t : Set β
ht : t ∈ fun s' => inst✝⁴.1 s'
⊢ IsOpen univ ∧ IsOpen t ∧ Prod.snd ⁻¹' t = univ ×ˢ t
simpa [Set.prod_eq] using ht