$\forall$$n$:$\mathbb{N}$, $f$, $g$:($\mathbb{N}$$_{\mbox{\scriptsize $<$$n$}}$$\rightarrow\mathbb{Z}$), $d$:$\mathbb{Z}$.
\\[0ex]sum($f$($x$)$-$$g$($x$) $\mid$ $x$ $<$ $n$) $=$ $d$ $\Rightarrow$ sum($f$($x$) $\mid$ $x$ $<$ $n$) $=$ sum($g$($x$) $\mid$ $x$ $<$ $n$)+$d$