English
Applying image after biUnion commutes: (s.image f).biUnion t = s.biUnion (λ a, t (f a)).
Русский
Применение образа после BiUnion совместимо: (s.image f).biUnion t = s.biUnion (λ a, t (f a)).
LaTeX
$$$\\bigl(s\\image f\\bigr)\\biUnion t = s.biUnion \\bigl(\\lambda a. t(f(a))\\bigr)$$$
Lean4
theorem image_biUnion [DecidableEq γ] {f : α → β} {s : Finset α} {t : β → Finset γ} :
(s.image f).biUnion t = s.biUnion fun a => t (f a) :=
haveI := Classical.decEq α
Finset.induction_on s rfl fun a s _ ih => by simp only [image_insert, biUnion_insert, ih]