English
For finite s ⊆ α and t ⊆ β and g: γ → δ, the infimum over image₂ f s t equals the iterated infimum with t outer: inf over y∈t of inf over x∈s of g(f(x,y)).
Русский
Для конечных s ⊆ α и t ⊆ β и g: γ → δ, инфимуум по image₂ f s t равен повторному инфимууму: inf_{y∈t} inf_{x∈s} g(f(x,y)).
LaTeX
$$$\inf (\operatorname{image}_2 f s t) g = \inf_{y \in t} \inf_{x \in s} g(f x y)$$$
Lean4
theorem inf_image₂_right (g : γ → δ) : inf (image₂ f s t) g = inf t fun y ↦ inf s (g <| f · y) :=
sup_image₂_right (δ := δᵒᵈ) ..