$\forall$$k$:$\mathbb{N}$, $f$, $g$:($\mathbb{N}$$_{\mbox{\scriptsize $<$$k$}}$$\rightarrow\mathbb{Z}$). ($\forall$$x$:$\mathbb{N}$$_{\mbox{\scriptsize $<$$k$}}$. $f$($x$)$\leq$$g$($x$)) $\Rightarrow$ sum($f$($x$) $\mid$ $x$ $<$ $k$)$\leq$sum($g$($x$) $\mid$ $x$ $<$ $k$)