English
If f, g, f', g' satisfy a right-commuting law: for all a,b,c, f(g(a,b), c) = g'(f'(a,c), b). Then image2 f (image2 g s t) u = image2 g' (image2 f' s u) t.
Русский
Пусть выполняется правое коммутирование: f(g(a,b), c) = g'(f'(a,c), b). Тогда image2 f (image2 g s t) u = image2 g' (image2 f' s u) t.
LaTeX
$$$\\forall a,b,c:\\ f(g(a,b), c) = g'(f'(a,c), b) \\Rightarrow \\operatorname{image}_2 f (\\operatorname{image}_2 g s t) u = \\operatorname{image}_2 g' (\\operatorname{image}_2 f' s u) t$$$
Lean4
theorem image2_comm {g : β → α → γ} (h_comm : ∀ a b, f a b = g b a) : image2 f s t = image2 g t s :=
(image2_swap _ _ _).trans <| by simp_rw [h_comm]
