English
For f, i, a, the image of Icc(a, f i) under update f i equals Icc(update f i a) (f i).
Русский
Для f, i, a образ Icc(a, f i) под обновлением f i равен Icc(update f i a) (f i).
LaTeX
$$$$ update f i '' Icc a (f i) = Icc (update f i a) f $$$$
Lean4
theorem image_update_Ioo (f : ∀ i, α i) (i : ι) (a b : α i) :
update f i '' Ioo a b = Ioo (update f i a) (update f i b) := by
rw [← Ico_diff_left, ← Ico_diff_left, image_diff (update_injective _ _), image_singleton, image_update_Ico]