mathlib-initiative/mathlib-tactics huggingface dataset:
Module: Mathlib.Topology.Sion

Goal state before:
pp: E : Type u_1
F : Type u_2
β : Type u_3
inst✝¹¹ : CompleteLinearOrder β
inst✝¹⁰ : DenselyOrdered β
X : Set E
Y : Set F
f : E → F → β
inst✝⁹ : TopologicalSpace E
inst✝⁸ : AddCommGroup E
inst✝⁷ : Module ℝ E
inst✝⁶ : IsTopologicalAddGroup E
inst✝⁵ : ContinuousSMul ℝ E
ne_X : X.Nonempty
cX : Convex ℝ X
kX : IsCompact X
hfy : ∀ y ∈ Y, LowerSemicontinuousOn (fun x ↦ f x y) X
hfy' : ∀ y ∈ Y, QuasiconvexOn ℝ X fun x ↦ f x y
inst✝⁴ : TopologicalSpace F
inst✝³ : AddCommGroup F
inst✝² : Module ℝ F
inst✝¹ : IsTopologicalAddGroup F
inst✝ : ContinuousSMul ℝ F
cY : Convex ℝ Y
ne_Y : Y.Nonempty
kY : IsCompact Y
hfx : ∀ x ∈ X, UpperSemicontinuousOn (fun y ↦ f x y) Y
hfx' : ∀ x ∈ X, QuasiconcaveOn ℝ Y fun y ↦ f x y
x : E
hx : x ∈ X
i : F
⊢ LowerSemicontinuousWithinAt (fun x1 ↦ ⨆ (_ : i ∈ Y), f x1 i) X x

Tactic:
exact lowerSemicontinuousWithinAt_iSup fun i_1 ↦ hfy i i_1 x hx

Goal state after: