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This note aims to give a short proof of the recent result due toEtg\"u--Lekili (2017) and Lekili--Ueda (2021): The zigzag algebra of any finiteconnected tree over a field of characteristic zero is intrinsically formal ifand only if the tree is of type ADE.

$A_\infty$-deformations of zigzag algebras via Ginzburg algebras