$\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($L$)) = $L_{2}$\}