$\forall$$g$:IGroup, $s$:($\mid$$g$$\mid\rightarrow\mathbb{P}$).
\\[0ex]($s$(e))
\\[0ex]$\Rightarrow$ ($\forall$$a$:$\mid$$g$$\mid$. ($s$($a$)) $\Rightarrow$ ($s$($\sim$($a$))))
\\[0ex]$\Rightarrow$ ($\forall$$a$, $b$:$\mid$$g$$\mid$. ($s$($a$)) $\Rightarrow$ ($s$($b$)) $\Rightarrow$ ($s$($a$ $\ast$ $b$)))
\\[0ex]$\Rightarrow$ EquivRel($\mid$$g$$\mid$;$x$,$y$.$x$ $\equiv$ $y$ (mod $s$ in $g$))