norm\_subset\_p($g$;$s$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$\forall$$a$:$\mid$$g$$\mid$, $b$:$\mid$$g$$\mid$. ($s$($b$)) $\Rightarrow$ ($s$((($\sim$$g$)($a$)) ($\ast$$g$) ($b$ ($\ast$$g$) $a$)))