$\forall$$T$:Type, ${\it eq}$, ${\it le}$:($T$$\rightarrow$$T$$\rightarrow\mathbb{B}$), ${\it op}$:($T$$\rightarrow$$T$$\rightarrow$$T$), ${\it id}$:$T$, ${\it inv}$:($T$$\rightarrow$$T$).
\\[0ex]IsEqFun($T$;${\it eq}$) $\Rightarrow$ Assoc($T$;${\it op}$) $\Rightarrow$ Ident($T$;${\it op}$;${\it id}$) $\Rightarrow$ ($<$$T$, ${\it eq}$, ${\it le}$, ${\it op}$, ${\it id}$, ${\it inv}$$>$ $\in$ Mon)