\begin{tabbing}
1. $T$ : Type
\\[0ex]2. $x$ : $T$
\\[0ex]3. $y$ : $T$
\\[0ex]4. $L_{1}$ : $T$ List
\\[0ex]5. $L_{2}$ : $T$ List
\\[0ex]6. $i$ : \{0..($\parallel$$L_{1}$ @ $L_{2}$$\parallel$ {-} 1)$^{-}$\}
\\[0ex]7. $x$ = ($L_{1}$ @ $L_{2}$)[$i$]
\\[0ex]8. $y$ = ($L_{1}$ @ $L_{2}$)[($i$+1)]
\\[0ex]9. $i$ $<$ $\parallel$$L_{1}$$\parallel$
\\[0ex]$\vdash$  \=($\exists$$i$:\{0..($\parallel$$L_{1}$$\parallel$ {-} 1)$^{-}$\}. ($x$ = $L_{1}$[$i$] \& $y$ = $L_{1}$[($i$+1)]))\+
\\[0ex]$\vee$ ((0 $<$ $\parallel$$L_{1}$$\parallel$) \& (0 $<$ $\parallel$$L_{2}$$\parallel$) \& $x$ = last($L_{1}$) \& $y$ = hd($L_{2}$))
\\[0ex]$\vee$ ($\exists$$i$:\{0..($\parallel$$L_{2}$$\parallel$ {-} 1)$^{-}$\}. ($x$ = $L_{2}$[$i$] \& $y$ = $L_{2}$[($i$+1)]))
\-
\end{tabbing}