$\forall$$n$:$\mathbb{N}$, $f$, $g$:($\mathbb{N}$$_{\mbox{\scriptsize $<$$n$}}$$\rightarrow\mathbb{Z}$). increasing($f$;$n$) $\Rightarrow$ nondecreasing($g$;$n$) $\Rightarrow$ increasing(fadd($f$;$g$);$n$)