$\forall$$T$:Type, $L$:$T$ List, $n$:$\mathbb{N}$, $f$:($\mathbb{N}$$_{\mbox{\scriptsize $<$$n$}}$$\rightarrow\mathbb{N}$$_{\mbox{\scriptsize $<\parallel$$L$$\parallel$}}$).
\\[0ex]increasing($f$;$n$) $\Rightarrow$ ($\exists$$L_{1}$:$T$ List. $\parallel$$L_{1}$$\parallel$ $=$ $n$ $\in$ $\mathbb{Z}$ \& sublist\_occurence($T$;$L_{1}$;$L$;$f$))