$\forall$$a$,$b$,$y_{1}$,$y_{2}$:$\mathbb{Z}$. gcd\_p($a$; $b$; $y_{1}$) $\Rightarrow$ gcd\_p($a$; $b$; $y_{2}$) $\Rightarrow$ assoced($y_{1}$; $y_{2}$)