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$\forall$$g$:IMonoid, $a$, $b$, $c$:$\mathbb{Z}$.
\\[0ex]($a$ $\leq$ $b$)
\\[0ex]$\Rightarrow$ ($b$ $\leq$ $c$)
\\[0ex]$\Rightarrow$ \=($\forall$$E$:(\{$a$..$c$$^{-}$\}$\rightarrow\mid$$g$$\mid$).\+
\\[0ex]($\Pi$ $a$ $\leq$ $j$ $<$ $c$. $E$($j$)) = (($\Pi$ $a$ $\leq$ $j$ $<$ $b$. $E$($j$)) $\ast$ ($\Pi$ $b$ $\leq$ $j$ $<$ $c$. $E$($j$))) $\in$ $\mid$$g$$\mid$)
\-
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