1. $T$ : Type
\\[0ex]2. $l_{1}$ : $T$ List
\\[0ex]3. $v$ : $T$
\\[0ex]4. $l_{2}$ : $T$ List
\\[0ex]5. $L$ : $T$ List
\\[0ex]6. $l_{2}$ = ($L$ @ $l_{1}$)
\\[0ex]7. $\parallel$$l_{1}$$\parallel$ $<$ $\parallel$$l_{2}$$\parallel$
\\[0ex]8. $l_{2}$[($\parallel$$l_{2}$$\parallel$ {-} ($\parallel$$l_{1}$$\parallel$+1))] = $v$
\\[0ex]9. $\neg$($\uparrow$null($L$))
\\[0ex]10. $\exists$${\it L'}$:$T$ List. ($L$ = (${\it L'}$ @ [last($L$)]))
\\[0ex]$\vdash$  $\exists$${\it L@}_{0}$:$T$ List. (($L$ @ $l_{1}$) = (${\it L@}_{0}$ @ [$v$ / $l_{1}$]))