Dung's semantics satisfy attack removal monotonicity

Formal argumentation theory [4] is nonmonotonic in the sense that when new arguments are added, some arguments may change their status. In this rapport, we show that preferred, stable, complete and grounded semantics satisfy attack removal monotonicity. This means that if an attack from b to a is removed, the status of a cannot worsen, e.g. if a was skeptically accepted, it cannot become rejected. Note that result we prove in the present document is the proof of Proposition 1 and Conjecture 1 of the recent paper by Amgoud et al. [2].