$\forall$$A$, $B$:Type, $f$:($A$$\rightarrow$$B$), $L$:$A$ List, $L_{2}$:$B$ List, $b$:$B$.
\\[0ex]map($f$;$L$) $=$ ($b$.$L_{2}$) $\Rightarrow$ \{$f$(hd($L$)) $=$ $b$ \& map($f$;tl($L$)) $=$ $L_{2}$\}