$\forall$$n$:$\mathbb{N}$, $x$:$\mathbb{Z}$, $f$:($\mathbb{N}$$_{\mbox{\scriptsize $<$$n$}}$$\rightarrow\mathbb{Z}$). increasing($f$;$n$) $\Rightarrow$ 0$<$$n$ $\Rightarrow$ $x$$<$$f$(0) $\Rightarrow$ increasing(fshift($f$;$x$);$n$+1)