intro b hb
α : Type u
β : Type v
inst✝³ : TopologicalSpace α
inst✝² : TopologicalSpace β
f : α → β
inst✝¹ : LinearOrder β
inst✝ : OrderClosedTopology β
g : α → β
s : Set α
a : α
hf : LowerSemicontinuousWithinAt f s a
hg : LowerSemicontinuousWithinAt g s a
⊢ LowerSemicontinuousWithinAt (fun x => f x ⊓ g x) s a
α : Type u
β : Type v
inst✝³ : TopologicalSpace α
inst✝² : TopologicalSpace β
f : α → β
inst✝¹ : LinearOrder β
inst✝ : OrderClosedTopology β
g : α → β
s : Set α
a : α
hf : LowerSemicontinuousWithinAt f s a
hg : LowerSemicontinuousWithinAt g s a
b : β
hb : b < (fun x => f x ⊓ g x) a
⊢ ∀ᶠ (x' : α) in 𝓝[s] a, b < (fun x => f x ⊓ g x) x'