\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{thm\_2EquantHeuristics\_2ELIST\_\_LENGTH\_\_5 (TMRszzmUTHivkr8bAAqpaZ3eKoMT1eK947v)}
\maketitle
\begin{definition}\label{def:dgpfcdfengjgogpfcdfepfddeepfddeepfddfe}
We define $\mname{c\_2Emin\_2E\_3D\_3D\_3E}$ to be ${{\uniddcgcg} P \in {2} .  {{\uniddcgcg} Q \in {2} .  {{inj\_\_o}~{({{{p}~{P}}{\unicdbdjdcd}{{p}~{Q}}})}}}}$ of type ${\iota}$.
\end{definition}
Let $ ty\_2Elist\_2Elist : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} A0 .  {{{nonempty}~{A0}}{\unicdbdjdcd}{{nonempty}~{({{ty\_2Elist\_2Elist}~{A0}})}}}}\label{hyp:ogfgpfehjhpfcdfemgjgdhehpfcdfemgjgdheh}
\end{equation}
Let $ c\_2Elist\_2ECONS : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}c\_2Elist\_2ECONS~A\_27a \in (((ty\_2Elist\_2Elist~\\
A\_27a)^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})^{{A\_27a}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfedepeoedf}
\end{equation}
Let $ ty\_2Enum\_2Enum : {\iota}$ be given.
Assume the following.
\begin{equation}
{{nonempty}~{ty\_2Enum\_2Enum}}\label{hyp:ogfgpfehjhpfcdfeogfhngpfcdfeogfhng}
\end{equation}
Let $ c\_2Earithmetic\_2EEVEN : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Earithmetic\_2EEVEN} \in {({{2}^{{ty\_2Enum\_2Enum}}})}}\label{hyp:ngfgngpfdgpfcdfebgchjgehigngfgehjgdgpfcdfefegffeoe}
\end{equation}
Let $ c\_2Earithmetic\_2EODD : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Earithmetic\_2EODD} \in {({{2}^{{ty\_2Enum\_2Enum}}})}}\label{hyp:ngfgngpfdgpfcdfebgchjgehigngfgehjgdgpfcdfepeeeee}
\end{equation}
Let $ c\_2Enum\_2EREP\_\_num : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Enum\_2EREP\_\_num} \in {({{omega}^{{ty\_2Enum\_2Enum}}})}}\label{hyp:ngfgngpfdgpfcdfeogfhngpfcdfecffeafpfpfogfhng}
\end{equation}
Let $ c\_2Enum\_2ESUC\_\_REP : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Enum\_2ESUC\_\_REP} \in {({{omega}^{{omega}}})}}\label{hyp:ngfgngpfdgpfcdfeogfhngpfcdfedfffdepfpfcffeaf}
\end{equation}
Let $ c\_2Enum\_2EABS\_\_num : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Enum\_2EABS\_\_num} \in {({{ty\_2Enum\_2Enum}^{{omega}}})}}\label{hyp:ngfgngpfdgpfcdfeogfhngpfcdfebecedfpfpfogfhng}
\end{equation}
\begin{definition}\label{def:dgpfcdfengjgogpfcdfepfddee}
We define $\mname{c\_2Emin\_2E\_3D}$ to be ${{\uniddcgcg} A .  {{\uniddcgcg} x \in {A} .  {{\uniddcgcg} y \in {A} .  {{inj\_\_o}~{({{x}={y}})}}}}}$ of type ${{\iota}{\unicdbdjdcd}{\iota}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfeef}
We define $\mname{c\_2Ebool\_2ET}$ to be ${({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{({{2}^{{2}}})}})}}~{({{\uniddcgcg} V0x \in {2} .  {V0x}})}})}}~{({{\uniddcgcg} V1x \in {2} .  {V1x}})}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepfcdbd}
We define $\mname{c\_2Ebool\_2E\_21}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {({{\uniddcgcg} V0P \in {({{2}^{{A\_27a}}})} .  {({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{({{2}^{{A\_27a}}})}})}}~{V0P}})}}~{({{\uniddcgcg} V1x \in {A\_27a} .  {\mname{c\_2Ebool\_2ET}}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfeogfhngpfcdfedfffde}
We define $\mname{c\_2Enum\_2ESUC}$ to be ${{\uniddcgcg} V0m \in {ty\_2Enum\_2Enum} .  {({{{ap}~{c\_2Enum\_2EABS\_\_num}}~{({{{ap}~{c\_2Enum\_2ESUC\_\_REP}}~{({{{ap}~{c\_2Enum\_2EREP\_\_num}}~{V0m}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfengjgogpfcdfepfedad}
We define $\mname{c\_2Emin\_2E\_40}$ to be ${{\uniddcgcg} A .  {{\uniddcgcg} P \in {{2}^{{A}}} .  {{\mathbf{if}}~{({{\unicdcdaddd} x \in {A} .  {{p}~{({{{ap}~{P}}~{x}})}}})}~{\mathbf{then}}~{({{the}~{({{\uniddcgcg} x .  {{{x} \in {A}}{\unicdcdcdhd}{{p}~{({{{ap}~{P}}~{x}})}}}})}})}~{\mathbf{else}}~{({{the}~{({{\uniddcgcg} x .  {{x} \in {A}}})}})}}}}$ of type ${{\iota}{\unicdbdjdcd}{\iota}}$.
\end{definition}
Let $ c\_2Enum\_2EZERO\_\_REP : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Enum\_2EZERO\_\_REP} \in {omega}}\label{hyp:ngfgngpfdgpfcdfeogfhngpfcdfekffecfpepfpfcffeaf}
\end{equation}
\begin{definition}\label{def:dgpfcdfeogfhngpfcdfead}
We define $\mname{c\_2Enum\_2E0}$ to be ${({{{ap}~{c\_2Enum\_2EABS\_\_num}}~{c\_2Enum\_2EZERO\_\_REP}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfege}
We define $\mname{c\_2Ebool\_2EF}$ to be ${({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{2}})}}~{({{\uniddcgcg} V0t \in {2} .  {V0t}})}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepfcdgepffdde}
We define $\mname{c\_2Ebool\_2E\_2F\_5C}$ to be ${({{\uniddcgcg} V0t1 \in {2} .  {({{\uniddcgcg} V1t2 \in {2} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{2}})}}~{({{\uniddcgcg} V2t \in {2} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V0t1}})}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V1t2}})}}~{V2t}})}})}})}}~{V2t}})}})}})}})}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfedepeoeee}
We define $\mname{c\_2Ebool\_2ECOND}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {({{\uniddcgcg} V0t \in {2} .  {({{\uniddcgcg} V1t1 \in {A\_27a} .  {({{\uniddcgcg} V2t2 \in {A\_27a} .  {({{{ap}~{({{\mname{c\_2Emin\_2E\_40}}~{A\_27a}})}}~{({{\uniddcgcg} V3x \in {A\_27a} .  {({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_2F\_5C}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{2}})}}~{V0t}})}}~{\mname{c\_2Ebool\_2ET}}})}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{A\_27a}})}}~{V3x}})}}~{V1t1}})}})}})}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{2}})}}~{V0t}})}}~{\mname{c\_2Ebool\_2EF}}})}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{A\_27a}})}}~{V3x}})}}~{V2t2}})}})}})}})}})}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfeahchjgngpfpfchfgdgpfcdfeafcffe}
We define $\mname{c\_2Eprim\_\_rec\_2EPRE}$ to be ${{\uniddcgcg} V0m \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V0m}})}}~{\mname{c\_2Enum\_2E0}}})}})}}~{\mname{c\_2Enum\_2E0}}})}}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_40}}~{ty\_2Enum\_2Enum}})}}~{({{\uniddcgcg} V1n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V0m}})}}~{({{{ap}~{\mname{c\_2Enum\_2ESUC}}}~{V1n}})}})}})}})}})}}$.
\end{definition}
Let $ c\_2Earithmetic\_2EEXP : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Earithmetic\_2EEXP \in ((ty\_2Enum\_2Enum^{{ty\_2Enum\_2Enum}})^{{ty\_2Enum\_2Enum}})\end{array}
\label{hyp:ngfgngpfdgpfcdfebgchjgehigngfgehjgdgpfcdfefeifaf}
\end{equation}
Let $ c\_2Earithmetic\_2E\_2A : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Earithmetic\_2E\_2A \in ((ty\_2Enum\_2Enum^{{ty\_2Enum\_2Enum}})^{{ty\_2Enum\_2Enum}})\end{array}
\label{hyp:ngfgngpfdgpfcdfebgchjgehigngfgehjgdgpfcdfepfcdbe}
\end{equation}
\begin{definition}\label{def:dgpfcdfeogfhngfgchbgmgpfcdfejgkf}
We define $\mname{c\_2Enumeral\_2EiZ}$ to be ${{\uniddcgcg} V0x \in {ty\_2Enum\_2Enum} .  {V0x}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepfhdfe}
We define $\mname{c\_2Ebool\_2E\_7E}$ to be ${({{\uniddcgcg} V0t \in {2} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V0t}})}}~{\mname{c\_2Ebool\_2EF}}})}})}$.
\end{definition}
Let $ c\_2Enumeral\_2EiSUB : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Enumeral\_2EiSUB \in (((ty\_2Enum\_2Enum^{{ty\_2Enum\_2Enum}})^{{ty\_2Enum\_2Enum}})^{{2}})\end{array}
\label{hyp:ngfgngpfdgpfcdfeogfhngfgchbgmgpfcdfejgdfffce}
\end{equation}
Let $ c\_2Earithmetic\_2E\_2D : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Earithmetic\_2E\_2D \in ((ty\_2Enum\_2Enum^{{ty\_2Enum\_2Enum}})^{{ty\_2Enum\_2Enum}})\end{array}
\label{hyp:ngfgngpfdgpfcdfebgchjgehigngfgehjgdgpfcdfepfcdee}
\end{equation}
Let $ c\_2Earithmetic\_2E\_2B : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Earithmetic\_2E\_2B \in ((ty\_2Enum\_2Enum^{{ty\_2Enum\_2Enum}})^{{ty\_2Enum\_2Enum}})\end{array}
\label{hyp:ngfgngpfdgpfcdfebgchjgehigngfgehjgdgpfcdfepfcdce}
\end{equation}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfecejeefcd}
We define $\mname{c\_2Earithmetic\_2EBIT2}$ to be ${{\uniddcgcg} V0n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{c\_2Earithmetic\_2E\_2B}}~{V0n}})}}~{({{{ap}~{({{{ap}~{c\_2Earithmetic\_2E\_2B}}~{V0n}})}}~{({{{ap}~{\mname{c\_2Enum\_2ESUC}}}~{({{{ap}~{\mname{c\_2Enum\_2ESUC}}}~{\mname{c\_2Enum\_2E0}}})}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfeogfhngfgchbgmgpfcdfejgeeffce}
We define $\mname{c\_2Enumeral\_2EiDUB}$ to be ${{\uniddcgcg} V0x \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{c\_2Earithmetic\_2E\_2B}}~{V0x}})}}~{V0x}})}}$.
\end{definition}
Let $ c\_2Elist\_2EAPPEND : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}c\_2Elist\_2EAPPEND~A\_27a \in (((ty\_2Elist\_2Elist~\\
A\_27a)^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfebeafaffeoeee}
\end{equation}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepfddge}
We define $\mname{c\_2Ebool\_2E\_3F}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {({{\uniddcgcg} V0P \in {({{2}^{{A\_27a}}})} .  {({{{ap}~{V0P}}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_40}}~{A\_27a}})}}~{V0P}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfeahchjgngpfpfchfgdgpfcdfepfddde}
We define $\mname{c\_2Eprim\_\_rec\_2E\_3C}$ to be ${{\uniddcgcg} V0m \in {ty\_2Enum\_2Enum} .  {{\uniddcgcg} V1n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_3F}}~{({{2}^{{ty\_2Enum\_2Enum}}})}})}}~{({{\uniddcgcg} V2P \in {({{2}^{{ty\_2Enum\_2Enum}}})} .  {({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_2F\_5C}}}~{({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{ty\_2Enum\_2Enum}})}}~{({{\uniddcgcg} V3n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{V2P}}~{({{{ap}~{\mname{c\_2Enum\_2ESUC}}}~{V3n}})}})}})}}~{({{{ap}~{V2P}}~{V3n}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_2F\_5C}}}~{({{{ap}~{V2P}}~{V0m}})}})}}~{({{{ap}~{\mname{c\_2Ebool\_2E\_7E}}}~{({{{ap}~{V2P}}~{V1n}})}})}})}})}})}})}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepffddepfcdge}
We define $\mname{c\_2Ebool\_2E\_5C\_2F}$ to be ${({{\uniddcgcg} V0t1 \in {2} .  {({{\uniddcgcg} V1t2 \in {2} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{2}})}}~{({{\uniddcgcg} V2t \in {2} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V0t1}})}}~{V2t}})}})}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V1t2}})}}~{V2t}})}})}}~{V2t}})}})}})}})}})}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfepfdddepfddee}
We define $\mname{c\_2Earithmetic\_2E\_3C\_3D}$ to be ${{\uniddcgcg} V0m \in {ty\_2Enum\_2Enum} .  {{\uniddcgcg} V1n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_5C\_2F}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Eprim\_\_rec\_2E\_3C}}}~{V0m}})}}~{V1n}})}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V0m}})}}~{V1n}})}})}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfepfddfe}
We define $\mname{c\_2Earithmetic\_2E\_3E}$ to be ${{\uniddcgcg} V0m \in {ty\_2Enum\_2Enum} .  {{\uniddcgcg} V1n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{\mname{c\_2Eprim\_\_rec\_2E\_3C}}}~{V1n}})}}~{V0m}})}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfepfddfepfddee}
We define $\mname{c\_2Earithmetic\_2E\_3E\_3D}$ to be ${{\uniddcgcg} V0m \in {ty\_2Enum\_2Enum} .  {{\uniddcgcg} V1n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_5C\_2F}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Earithmetic\_2E\_3E}}}~{V0m}})}}~{V1n}})}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V0m}})}}~{V1n}})}})}}}$.
\end{definition}
Let $ c\_2Elist\_2ENIL : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}c\_2Elist\_2ENIL~A\_27a \in (ty\_2Elist\_2Elist~\\
A\_27a)\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfeoejeme}
\end{equation}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfekffecfpe}
We define $\mname{c\_2Earithmetic\_2EZERO}$ to be ${\mname{c\_2Enum\_2E0}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfecejeefbd}
We define $\mname{c\_2Earithmetic\_2EBIT1}$ to be ${{\uniddcgcg} V0n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{c\_2Earithmetic\_2E\_2B}}~{V0n}})}}~{({{{ap}~{({{{ap}~{c\_2Earithmetic\_2E\_2B}}~{V0n}})}}~{({{{ap}~{\mname{c\_2Enum\_2ESUC}}}~{\mname{c\_2Enum\_2E0}}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfeoeffnefecfbeme}
We define $\mname{c\_2Earithmetic\_2ENUMERAL}$ to be ${{\uniddcgcg} V0x \in {ty\_2Enum\_2Enum} .  {V0x}}$.
\end{definition}
Let $ c\_2Elist\_2ELENGTH : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}c\_2Elist\_2ELENGTH~A\_27a \in (ty\_2Enum\_2Enum^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfemefeoeheefie}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0m \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1n \in ty\_2Enum\_2Enum .  (\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~V0m)~V1n)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1n)~V0m))))\end{array}
\label{hyp:ehigngpfcdfebgchjgehigngfgehjgdgpfcdfebeeeeepfpfdfjfne}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0m \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1n \in ty\_2Enum\_2Enum .  (\\
(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~V0m)~V1n)){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~\mname{c\_2Enum\_2ESUC}~V0m))~V1n)))))\end{array}
\label{hyp:ehigngpfcdfebgchjgehigngfgehjgdgpfcdfemefedfdfpfpffebf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0c \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2D~V0c)~\\
V0c)=\mname{c\_2Enum\_2E0}))\end{array}
\label{hyp:ehigngpfcdfebgchjgehigngfgehjgdgpfcdfedfffcepfpffebfffbemepfpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1m \in ty\_2Enum\_2Enum .  (\\
(p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~V0n)~V1m)){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1m)~V0n)))))\end{array}
\label{hyp:ehigngpfcdfebgchjgehigngfgehjgdgpfcdfehecffebeeffecfpfpffebf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0t1 \in 2 .  ({\unicdcdadad} V1t2 \in 2 .  (((p~V0t1){\unicdbdjdcd}(p~V1t2)){\unicdbdjdcd}(((p~\\
V1t2){\unicdbdjdcd}(p~V0t1)){\unicdbdjdcd}((p~V0t1){\unicdbdjded}(p~V1t2))))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfejeneafpfpfbeoeefjedfjfnepfpfbeif}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0x \in A\_27a .  ({\unicdcdadad} V1y \in \\
A\_27a .  ((V0x=V1y){\unicdbdjded}(V1y=V0x))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfefebfpfpfdfjfnepfpffebf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0t1 \in A\_27a .  ({\unicdcdadad} V1t2 \in \\
A\_27a .  (((ap~(ap~(ap~(\mname{c\_2Ebool\_2ECOND}~A\_27a)~\mname{c\_2Ebool\_2ET})~V0t1)~\\
V1t2)=V0t1){\unicdcdcdhd}((ap~(ap~(ap~(\mname{c\_2Ebool\_2ECOND}~A\_27a)~\mname{c\_2Ebool\_2EF})~\\
V0t1)~V1t2)=V1t2))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfedepeoeeepfpfdemebeffdffedf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0P \in (2^{{A\_27a}}) .  ({\unicdcdadad} V1Q \in \\
2 .  (({\unicdcdaddd} V2x \in A\_27a .  ((p~(ap~V0P~V2x)){\unicdcdcdhd}(p~V1Q))){\unicdbdjded}(({\unicdcdaddd} V3x \in \\
A\_27a .  (p~(ap~V0P~V3x))){\unicdcdcdhd}(p~V1Q)))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfemefegeefpfpffeifjedfefdfpfpfbeoeeepfpfefiene}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0P \in (2^{{A\_27a}}) .  ({\unicdcdadad} V1a \in \\
A\_27a .  (({\unicdcdaddd} V2x \in A\_27a .  ((V2x=V1a){\unicdcdcdhd}(p~(ap~V0P~V2x)))){\unicdbdjded}(p~(\\
ap~V0P~V1a)))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfeffoehfjeoeeepfpfefienecd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}(({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ((ap~(ap~(c\_2Elist\_2EAPPEND~A\_27a)~(c\_2Elist\_2ENIL~A\_27a))~\\
V0l)=V0l)){\unicdcdcdhd}({\unicdcdadad} V1l1 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdadad} V2l2 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdadad} V3h \in A\_27a .  ((ap~(ap~(c\_2Elist\_2EAPPEND~\\
A\_27a)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V3h)~V1l1))~V2l2)=(ap~(ap~\\
(c\_2Elist\_2ECONS~A\_27a)~V3h)~(ap~(ap~(c\_2Elist\_2EAPPEND~A\_27a)~\\
V1l1)~V2l2)))))))\end{array}
\label{hyp:ehigngpfcdfemgjgdhehpfcdfebeafaffeoeee}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=\mname{c\_2Enum\_2E0}){\unicdbdjded}(\\
V0l=(c\_2Elist\_2ENIL~A\_27a))))\end{array}
\label{hyp:ehigngpfcdfemgjgdhehpfcdfemefeoeheefiepfpfoejeme}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}(({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=\mname{c\_2Enum\_2E0}){\unicdbdjded}(\\
V0l=(c\_2Elist\_2ENIL~A\_27a)))){\unicdcdcdhd}(({\unicdcdadad} V1l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdadad} V2n \in ty\_2Enum\_2Enum .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V1l)=(ap~\mname{c\_2Enum\_2ESUC}~V2n)){\unicdbdjded}({\unicdcdaddd} V3h \in A\_27a .  ({\unicdcdaddd} V4l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V4l\_27)=\\
V2n){\unicdcdcdhd}(V1l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V3h)~V4l\_27)))))))){\unicdcdcdhd}\\
({\unicdcdadad} V5l \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdadad} V6n1 \in ty\_2Enum\_2Enum .  \\
({\unicdcdadad} V7n2 \in ty\_2Enum\_2Enum .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V5l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~V6n1)~V7n2)){\unicdbdjded}({\unicdcdaddd} V8l1 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V9l2 \in (ty\_2Elist\_2Elist~A\_27a) .  \\
(((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V8l1)=V6n1){\unicdcdcdhd}(((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V9l2)=V7n2){\unicdcdcdhd}(V5l=(ap~(ap~(c\_2Elist\_2EAPPEND~A\_27a)~V8l1)~\\
V9l2))))))))))))\end{array}
\label{hyp:ehigngpfcdfemgjgdhehpfcdfemefeoeheefiepfpffebfpfpfoeffne}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}(({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=\mname{c\_2Enum\_2E0}){\unicdbdjded}(\\
V0l=(c\_2Elist\_2ENIL~A\_27a)))){\unicdcdcdhd}(({\unicdcdadad} V1l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdadad} V2n \in ty\_2Enum\_2Enum .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V1l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V2n))){\unicdbdjded}({\unicdcdaddd} V3h \in A\_27a .  ({\unicdcdaddd} V4l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V4l\_27)=(ap~(ap~c\_2Earithmetic\_2E\_2D~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V2n)))~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdcdcdhd}\\
(V1l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V3h)~V4l\_27)))))))){\unicdcdcdhd}(({\unicdcdadad} V5l \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdadad} V6n \in ty\_2Enum\_2Enum .  (((ap~\\
(c\_2Elist\_2ELENGTH~A\_27a)~V5l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~V6n))){\unicdbdjded}({\unicdcdaddd} V7h \in A\_27a .  ({\unicdcdaddd} V8l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V8l\_27)=\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V6n))){\unicdcdcdhd}\\
(V5l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V7h)~V8l\_27)))))))){\unicdcdcdhd}({\unicdcdadad} V9l \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdadad} V10n1 \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V11n2 \in \\
ty\_2Enum\_2Enum .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V9l)=(ap~(ap~\\
c\_2Earithmetic\_2E\_2B~V10n1)~V11n2)){\unicdbdjded}({\unicdcdaddd} V12l1 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V13l2 \in (ty\_2Elist\_2Elist~A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V12l1)=V10n1){\unicdcdcdhd}(((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V13l2)=\\
V11n2){\unicdcdcdhd}(V9l=(ap~(ap~(c\_2Elist\_2EAPPEND~A\_27a)~V12l1)~V13l2)))))))))))))\end{array}
\label{hyp:ehigngpfcdfemgjgdhehpfcdfemefeoeheefiepfpffebfpfpfoeffnepfpfdgpgngahfhehfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(((ap~\mname{c\_2Enum\_2ESUC}~\mname{c\_2Earithmetic\_2EZERO})=(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO})){\unicdcdcdhd}(({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ((ap~\\
\mname{c\_2Enum\_2ESUC}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V0n))=(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V0n))){\unicdcdcdhd}({\unicdcdadad} V1n \in ty\_2Enum\_2Enum .  ((ap~\mname{c\_2Enum\_2ESUC}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V1n))=(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Enum\_2ESUC}~V1n))))))\end{array}
\label{hyp:ehigngpfcdfeogfhngfgchbgmgpfcdfeogfhngfgchbgmgpfpfdhfhdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2B~\\
\mname{c\_2Enum\_2E0})~V0n)=V0n)){\unicdcdcdhd}(({\unicdcdadad} V1n \in ty\_2Enum\_2Enum .  ((ap~\\
(ap~c\_2Earithmetic\_2E\_2B~V1n)~\mname{c\_2Enum\_2E0})=V1n)){\unicdcdcdhd}(({\unicdcdadad} V2n \in \\
ty\_2Enum\_2Enum .  ({\unicdcdadad} V3m \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V2n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V3m))=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Enumeral\_2EiZ}~(ap~\\
(ap~c\_2Earithmetic\_2E\_2B~V2n)~V3m)))))){\unicdcdcdhd}(({\unicdcdadad} V4n \in ty\_2Enum\_2Enum .  \\
((ap~(ap~c\_2Earithmetic\_2E\_2A~\mname{c\_2Enum\_2E0})~V4n)=\mname{c\_2Enum\_2E0})){\unicdcdcdhd}\\
(({\unicdcdadad} V5n \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2A~\\
V5n)~\mname{c\_2Enum\_2E0})=\mname{c\_2Enum\_2E0})){\unicdcdcdhd}(({\unicdcdadad} V6n \in ty\_2Enum\_2Enum .  \\
({\unicdcdadad} V7m \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2A~(\\
ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V6n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V7m))=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~(ap~c\_2Earithmetic\_2E\_2A~\\
V6n)~V7m))))){\unicdcdcdhd}(({\unicdcdadad} V8n \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2D~\\
\mname{c\_2Enum\_2E0})~V8n)=\mname{c\_2Enum\_2E0})){\unicdcdcdhd}(({\unicdcdadad} V9n \in ty\_2Enum\_2Enum .  \\
((ap~(ap~c\_2Earithmetic\_2E\_2D~V9n)~\mname{c\_2Enum\_2E0})=V9n)){\unicdcdcdhd}(({\unicdcdadad} V10n \in \\
ty\_2Enum\_2Enum .  ({\unicdcdadad} V11m \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2E\_2D~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V10n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V11m))=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~(ap~c\_2Earithmetic\_2E\_2D~\\
V10n)~V11m))))){\unicdcdcdhd}(({\unicdcdadad} V12n \in ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2EEXP~\\
\mname{c\_2Enum\_2E0})~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V12n)))=\mname{c\_2Enum\_2E0})){\unicdcdcdhd}(({\unicdcdadad} V13n \in ty\_2Enum\_2Enum .  ((ap~\\
(ap~c\_2Earithmetic\_2EEXP~\mname{c\_2Enum\_2E0})~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~V13n)))=\mname{c\_2Enum\_2E0})){\unicdcdcdhd}(({\unicdcdadad} V14n \in \\
ty\_2Enum\_2Enum .  ((ap~(ap~c\_2Earithmetic\_2EEXP~V14n)~\mname{c\_2Enum\_2E0})=\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdcdcdhd}\\
(({\unicdcdadad} V15n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V16m \in ty\_2Enum\_2Enum .  \\
((ap~(ap~c\_2Earithmetic\_2EEXP~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V15n))~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V16m))=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~(ap~c\_2Earithmetic\_2EEXP~V15n)~V16m))))){\unicdcdcdhd}(((ap~\mname{c\_2Enum\_2ESUC}~\\
\mname{c\_2Enum\_2E0})=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))){\unicdcdcdhd}(({\unicdcdadad} V17n \in ty\_2Enum\_2Enum .  (\\
(ap~\mname{c\_2Enum\_2ESUC}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V17n))=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Enum\_2ESUC}~V17n)))){\unicdcdcdhd}(((ap~\mname{c\_2Eprim\_\_rec\_2EPRE}~\mname{c\_2Enum\_2E0})=\\
\mname{c\_2Enum\_2E0}){\unicdcdcdhd}(({\unicdcdadad} V18n \in ty\_2Enum\_2Enum .  ((ap~\mname{c\_2Eprim\_\_rec\_2EPRE}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V18n))=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Eprim\_\_rec\_2EPRE}~V18n)))){\unicdcdcdhd}(({\unicdcdadad} V19n \in ty\_2Enum\_2Enum .  \\
(((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V19n)=\mname{c\_2Enum\_2E0}){\unicdbdjded}(V19n=\mname{c\_2Earithmetic\_2EZERO}))){\unicdcdcdhd}\\
(({\unicdcdadad} V20n \in ty\_2Enum\_2Enum .  ((\mname{c\_2Enum\_2E0}=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V20n)){\unicdbdjded}(V20n=\mname{c\_2Earithmetic\_2EZERO}))){\unicdcdcdhd}(({\unicdcdadad} V21n \in ty\_2Enum\_2Enum .  \\
({\unicdcdadad} V22m \in ty\_2Enum\_2Enum .  (((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V21n)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V22m)){\unicdbdjded}(V21n=V22m)))){\unicdcdcdhd}\\
(({\unicdcdadad} V23n \in ty\_2Enum\_2Enum .  ((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
V23n)~\mname{c\_2Enum\_2E0})){\unicdbdjded}False)){\unicdcdcdhd}(({\unicdcdadad} V24n \in ty\_2Enum\_2Enum .  \\
((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\mname{c\_2Enum\_2E0})~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V24n))){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\mname{c\_2Earithmetic\_2EZERO})~\\
V24n)))){\unicdcdcdhd}(({\unicdcdadad} V25n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V26m \in ty\_2Enum\_2Enum .  \\
((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V25n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V26m))){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
V25n)~V26m))))){\unicdcdcdhd}(({\unicdcdadad} V27n \in ty\_2Enum\_2Enum .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~\\
\mname{c\_2Enum\_2E0})~V27n)){\unicdbdjded}False)){\unicdcdcdhd}(({\unicdcdadad} V28n \in ty\_2Enum\_2Enum .  \\
((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V28n))~\mname{c\_2Enum\_2E0})){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\mname{c\_2Earithmetic\_2EZERO})~\\
V28n)))){\unicdcdcdhd}(({\unicdcdadad} V29n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V30m \in ty\_2Enum\_2Enum .  \\
((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V29n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V30m))){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
V30m)~V29n))))){\unicdcdcdhd}(({\unicdcdadad} V31n \in ty\_2Enum\_2Enum .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
\mname{c\_2Enum\_2E0})~V31n)){\unicdbdjded}True)){\unicdcdcdhd}(({\unicdcdadad} V32n \in ty\_2Enum\_2Enum .  \\
((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V32n))~\mname{c\_2Enum\_2E0})){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V32n)~\\
\mname{c\_2Earithmetic\_2EZERO})))){\unicdcdcdhd}(({\unicdcdadad} V33n \in ty\_2Enum\_2Enum .  \\
({\unicdcdadad} V34m \in ty\_2Enum\_2Enum .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V33n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V34m))){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V33n)~V34m))))){\unicdcdcdhd}(\\
({\unicdcdadad} V35n \in ty\_2Enum\_2Enum .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
V35n)~\mname{c\_2Enum\_2E0})){\unicdbdjded}True)){\unicdcdcdhd}(({\unicdcdadad} V36n \in ty\_2Enum\_2Enum .  \\
((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\mname{c\_2Enum\_2E0})~V36n)){\unicdbdjded}(V36n=\\
\mname{c\_2Enum\_2E0}))){\unicdcdcdhd}(({\unicdcdadad} V37n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V38m \in \\
ty\_2Enum\_2Enum .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
V37n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V38m))){\unicdbdjded}(p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V38m)~V37n))))){\unicdcdcdhd}(({\unicdcdadad} V39n \in ty\_2Enum\_2Enum .  ((p~(ap~c\_2Earithmetic\_2EODD~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V39n))){\unicdbdjded}(p~(ap~c\_2Earithmetic\_2EODD~\\
V39n)))){\unicdcdcdhd}(({\unicdcdadad} V40n \in ty\_2Enum\_2Enum .  ((p~(ap~c\_2Earithmetic\_2EEVEN~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~V40n))){\unicdbdjded}(p~(ap~c\_2Earithmetic\_2EEVEN~\\
V40n)))){\unicdcdcdhd}((\preoh (p~(ap~c\_2Earithmetic\_2EODD~\mname{c\_2Enum\_2E0}))){\unicdcdcdhd}(p~(\\
ap~c\_2Earithmetic\_2EEVEN~\mname{c\_2Enum\_2E0})))))))))))))))))))))))))))))))))))))\end{array}
\label{hyp:ehigngpfcdfeogfhngfgchbgmgpfcdfeogfhngfgchbgmgpfpfegjgdhehchjgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1m \in ty\_2Enum\_2Enum .  (\\
((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\mname{c\_2Earithmetic\_2EZERO})~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V0n))){\unicdbdjded}True){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\mname{c\_2Earithmetic\_2EZERO})~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~V0n))){\unicdbdjded}True){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
V0n)~\mname{c\_2Earithmetic\_2EZERO})){\unicdbdjded}False){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~V0n))~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V1m))){\unicdbdjded}\\
(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~V0n)~V1m))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~V0n))~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V1m))){\unicdbdjded}\\
(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~V0n)~V1m))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~V0n))~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V1m))){\unicdbdjded}\\
(\preoh (p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~V1m)~V0n)))){\unicdcdcdhd}((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~V0n))~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V1m))){\unicdbdjded}\\
(p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~V0n)~V1m)))))))))))\end{array}
\label{hyp:ehigngpfcdfeogfhngfgchbgmgpfcdfeogfhngfgchbgmgpfpfmgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0x \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1b \in 2 .  ({\unicdcdadad} V2n \in ty\_2Enum\_2Enum .  \\
({\unicdcdadad} V3m \in ty\_2Enum\_2Enum .  (((ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\\
V1b)~\mname{c\_2Earithmetic\_2EZERO})~V0x)=\mname{c\_2Earithmetic\_2EZERO}){\unicdcdcdhd}(\\
((ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~V2n)~\mname{c\_2Earithmetic\_2EZERO})=\\
V2n){\unicdcdcdhd}(((ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V2n))~\mname{c\_2Earithmetic\_2EZERO})=(ap~\mname{c\_2Enumeral\_2EiDUB}~V2n)){\unicdcdcdhd}\\
(((ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V3m))=(ap~\mname{c\_2Enumeral\_2EiDUB}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~V2n)~V3m))){\unicdcdcdhd}(((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V3m))=(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~V2n)~V3m))){\unicdcdcdhd}(((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V3m))=(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~V2n)~V3m))){\unicdcdcdhd}(((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V3m))=(ap~\mname{c\_2Enumeral\_2EiDUB}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~V2n)~V3m))){\unicdcdcdhd}(((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V2n))~\mname{c\_2Earithmetic\_2EZERO})=(ap~\mname{c\_2Earithmetic\_2EBIT1}~V2n)){\unicdcdcdhd}\\
(((ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V3m))=(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~V2n)~V3m))){\unicdcdcdhd}(((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V3m))=(ap~\mname{c\_2Enumeral\_2EiDUB}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~V2n)~V3m))){\unicdcdcdhd}(((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V3m))=(ap~\mname{c\_2Enumeral\_2EiDUB}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2ET})~V2n)~V3m))){\unicdcdcdhd}((ap~\\
(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
V2n))~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V3m))=(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\mname{c\_2Ebool\_2EF})~V2n)~V3m))))))))))))))))))\end{array}
\label{hyp:ehigngpfcdfeogfhngfgchbgmgpfcdfejgdfffcepfpfefiene}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1m \in ty\_2Enum\_2Enum .  (\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~(ap~c\_2Earithmetic\_2E\_2D~V0n)~\\
V1m))=(ap~(ap~(ap~(\mname{c\_2Ebool\_2ECOND}~ty\_2Enum\_2Enum)~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
V1m)~V0n))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~(ap~(ap~c\_2Enumeral\_2EiSUB~\\
\mname{c\_2Ebool\_2ET})~V0n)~V1m)))~\mname{c\_2Enum\_2E0}))))\end{array}
\label{hyp:ehigngpfcdfeogfhngfgchbgmgpfcdfeogfhngfgchbgmgpfpfdhfhcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  (((ap~\mname{c\_2Enumeral\_2EiDUB}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
V0n))=(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Enumeral\_2EiDUB}~V0n))){\unicdcdcdhd}\\
(((ap~\mname{c\_2Enumeral\_2EiDUB}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~V0n))=(ap~\\
\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~V0n))){\unicdcdcdhd}((ap~\\
\mname{c\_2Enumeral\_2EiDUB}~\mname{c\_2Earithmetic\_2EZERO})=\mname{c\_2Earithmetic\_2EZERO}))))\end{array}
\label{hyp:ehigngpfcdfeogfhngfgchbgmgpfcdfejgeeffcepfpfchfgngpgghbgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  (\\
{\unicdcdadad} V1m \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V2l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V0n)~V1m))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V2l))){\unicdbdjded}({\unicdcdaddd} V3l1 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V4l2 \in (ty\_2Elist\_2Elist~A\_27a) .  \\
(((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V3l1)=V0n){\unicdcdcdhd}((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1m)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V4l2))){\unicdcdcdhd}(V2l=(ap~(ap~(c\_2Elist\_2EAPPEND~\\
A\_27a)~V3l1)~V4l2))))))))))\end{array}
\label{hyp:ehigngpfcdfebhfhbgogehiefgfhchjgdhehjgdgdhpfcdfemefeoeheefiepfpfmefepfpfafmeffdf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  (\\
{\unicdcdadad} V1l \in (ty\_2Elist\_2Elist~A\_27a) .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V0n)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V1l))){\unicdbdjded}({\unicdcdaddd} V2l1 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V3l2 \in (ty\_2Elist\_2Elist~A\_27a) .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V2l1)=V0n){\unicdcdcdhd}(V1l=(ap~(ap~(c\_2Elist\_2EAPPEND~A\_27a)~V2l1)~\\
V3l2))))))))\end{array}
\label{hyp:ehigngpfcdfebhfhbgogehiefgfhchjgdhehjgdgdhpfcdfemefeoeheefiepfpfmefepfpfoeffne}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ((\mname{c\_2Enum\_2E0}=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}(\\
V0l=(c\_2Elist\_2ENIL~A\_27a))))\end{array}
\label{hyp:ehigngpfcdfebhfhbgogehiefgfhchjgdhehjgdgdhpfcdfemefeoeheefiepfpfoejemepfpfdfjfne}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  (((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~A\_27a))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~A\_27a))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
\mname{c\_2Enum\_2E0})~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~\\
A\_27a))){\unicdcdcdhd}((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))~\mname{c\_2Enum\_2E0})){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~A\_27a)))))))\end{array}
\label{hyp:ehigngpfcdfebhfhbgogehiefgfhchjgdhehjgdgdhpfcdfemejedfefpfpfmefeoeheefiepfpfdepeneafbecffepfpfbd}
\end{equation}
\begin{theorem}\label{thm:ehigngpfcdfebhfhbgogehiefgfhchjgdhehjgdgdhpfcdfemejedfefpfpfmefeoeheefiepfpffd}
$$\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdadad} V1x \in ty\_2Enum\_2Enum .  ((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V2e1 \in \\
A\_27a .  ({\unicdcdaddd} V3e2 \in A\_27a .  ({\unicdcdaddd} V4e3 \in A\_27a .  ({\unicdcdaddd} V5e4 \in \\
A\_27a .  ({\unicdcdaddd} V6e5 \in A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V2e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V3e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V4e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V5e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V6e5)~(c\_2Elist\_2ENIL~A\_27a))))))))))))){\unicdcdcdhd}((((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))=\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V7e1 \in A\_27a .  ({\unicdcdaddd} V8e2 \in \\
A\_27a .  ({\unicdcdaddd} V9e3 \in A\_27a .  ({\unicdcdaddd} V10e4 \in A\_27a .  ({\unicdcdaddd} V11e5 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V7e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V8e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V9e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V10e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V11e5)~(c\_2Elist\_2ENIL~\\
A\_27a))))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V12l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V13e1 \in A\_27a .  ({\unicdcdaddd} V14e2 \in A\_27a .  ({\unicdcdaddd} V15e3 \in \\
A\_27a .  ({\unicdcdaddd} V16e4 \in A\_27a .  ({\unicdcdaddd} V17e5 \in A\_27a .  (V0l=(ap~(\\
ap~(c\_2Elist\_2ECONS~A\_27a)~V13e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V14e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V15e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V16e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V17e5)~V12l\_27))))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V18l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V19e1 \in A\_27a .  ({\unicdcdaddd} V20e2 \in \\
A\_27a .  ({\unicdcdaddd} V21e3 \in A\_27a .  ({\unicdcdaddd} V22e4 \in A\_27a .  ({\unicdcdaddd} V23e5 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V19e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V20e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V21e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V22e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V23e5)~V18l\_27))))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V24l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V25e1 \in A\_27a .  ({\unicdcdaddd} V26e2 \in A\_27a .  ({\unicdcdaddd} V27e3 \in \\
A\_27a .  ({\unicdcdaddd} V28e4 \in A\_27a .  ({\unicdcdaddd} V29e5 \in A\_27a .  (V0l=(ap~(\\
ap~(c\_2Elist\_2ECONS~A\_27a)~V25e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V26e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V27e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V28e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V29e5)~V24l\_27))))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V30l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V31e1 \in A\_27a .  ({\unicdcdaddd} V32e2 \in \\
A\_27a .  ({\unicdcdaddd} V33e3 \in A\_27a .  ({\unicdcdaddd} V34e4 \in A\_27a .  ({\unicdcdaddd} V35e5 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V31e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V32e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V33e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V34e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V35e5)~V30l\_27))))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~V1x))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))){\unicdbdjded}({\unicdcdaddd} V36l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V37e1 \in \\
A\_27a .  ({\unicdcdaddd} V38e2 \in A\_27a .  ({\unicdcdaddd} V39e3 \in A\_27a .  ({\unicdcdaddd} V40e4 \in \\
A\_27a .  ({\unicdcdaddd} V41e5 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V36l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V37e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V38e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V39e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V40e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V41e5)~V36l\_27)))))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~V1x))){\unicdbdjded}({\unicdcdaddd} V42l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V43e1 \in A\_27a .  ({\unicdcdaddd} V44e2 \in A\_27a .  ({\unicdcdaddd} V45e3 \in \\
A\_27a .  ({\unicdcdaddd} V46e4 \in A\_27a .  ({\unicdcdaddd} V47e5 \in A\_27a .  ((p~(ap~(ap~\\
\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V42l\_27))){\unicdcdcdhd}\\
(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V43e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V44e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V45e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V46e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V47e5)~V42l\_27)))))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))))~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V48l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V49e1 \in \\
A\_27a .  ({\unicdcdaddd} V50e2 \in A\_27a .  ({\unicdcdaddd} V51e3 \in A\_27a .  ({\unicdcdaddd} V52e4 \in \\
A\_27a .  ({\unicdcdaddd} V53e5 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V48l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V49e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V50e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V51e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V52e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V53e5)~V48l\_27)))))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))))){\unicdbdjded}({\unicdcdaddd} V54l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V55e1 \in A\_27a .  ({\unicdcdaddd} V56e2 \in \\
A\_27a .  ({\unicdcdaddd} V57e3 \in A\_27a .  ({\unicdcdaddd} V58e4 \in A\_27a .  ({\unicdcdaddd} V59e5 \in \\
A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V54l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V55e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V56e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V57e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V58e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V59e5)~V54l\_27)))))))))))))){\unicdcdcdhd}((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
V1x)){\unicdbdjded}({\unicdcdaddd} V60l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V61e1 \in \\
A\_27a .  ({\unicdcdaddd} V62e2 \in A\_27a .  ({\unicdcdaddd} V63e3 \in A\_27a .  ({\unicdcdaddd} V64e4 \in \\
A\_27a .  ({\unicdcdaddd} V65e5 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V60l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V61e1)~(ap~\\
(ap~(c\_2Elist\_2ECONS~A\_27a)~V62e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V63e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V64e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V65e5)~V60l\_27)))))))))))))){\unicdcdcdhd}((((ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~V1x)=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l)){\unicdbdjded}({\unicdcdaddd} V66l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V67e1 \in \\
A\_27a .  ({\unicdcdaddd} V68e2 \in A\_27a .  ({\unicdcdaddd} V69e3 \in A\_27a .  ({\unicdcdaddd} V70e4 \in \\
A\_27a .  ({\unicdcdaddd} V71e5 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V66l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V67e1)~(ap~\\
(ap~(c\_2Elist\_2ECONS~A\_27a)~V68e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V69e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V70e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V71e5)~V66l\_27)))))))))))))){\unicdcdcdhd}((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}\\
({\unicdcdaddd} V72l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V73e1 \in A\_27a .  \\
({\unicdcdaddd} V74e2 \in A\_27a .  ({\unicdcdaddd} V75e3 \in A\_27a .  ({\unicdcdaddd} V76e4 \in A\_27a .  \\
({\unicdcdaddd} V77e5 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V72l\_27)=\\
V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V73e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V74e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V75e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V76e4)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V77e5)~V72l\_27)))))))))))))){\unicdcdcdhd}\\
((((ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))))=\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V78l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V79e1 \in A\_27a .  ({\unicdcdaddd} V80e2 \in A\_27a .  ({\unicdcdaddd} V81e3 \in \\
A\_27a .  ({\unicdcdaddd} V82e4 \in A\_27a .  ({\unicdcdaddd} V83e5 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V78l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V79e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V80e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V81e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V82e4)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V83e5)~V78l\_27)))))))))))))){\unicdcdcdhd}((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V84e1 \in \\
A\_27a .  ({\unicdcdaddd} V85e2 \in A\_27a .  ({\unicdcdaddd} V86e3 \in A\_27a .  ({\unicdcdaddd} V87e4 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V84e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V85e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V86e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V87e4)~(c\_2Elist\_2ENIL~A\_27a))))))))))){\unicdcdcdhd}((((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))=\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V88e1 \in A\_27a .  ({\unicdcdaddd} V89e2 \in \\
A\_27a .  ({\unicdcdaddd} V90e3 \in A\_27a .  ({\unicdcdaddd} V91e4 \in A\_27a .  (V0l=(ap~(\\
ap~(c\_2Elist\_2ECONS~A\_27a)~V88e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V89e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V90e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V91e4)~(c\_2Elist\_2ENIL~A\_27a))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}\\
({\unicdcdaddd} V92l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V93e1 \in A\_27a .  \\
({\unicdcdaddd} V94e2 \in A\_27a .  ({\unicdcdaddd} V95e3 \in A\_27a .  ({\unicdcdaddd} V96e4 \in A\_27a .  \\
(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V93e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V94e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V95e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V96e4)~V92l\_27))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}\\
({\unicdcdaddd} V97l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V98e1 \in A\_27a .  \\
({\unicdcdaddd} V99e2 \in A\_27a .  ({\unicdcdaddd} V100e3 \in A\_27a .  ({\unicdcdaddd} V101e4 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V98e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V99e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V100e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V101e4)~V97l\_27))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}\\
({\unicdcdaddd} V102l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V103e1 \in \\
A\_27a .  ({\unicdcdaddd} V104e2 \in A\_27a .  ({\unicdcdaddd} V105e3 \in A\_27a .  ({\unicdcdaddd} V106e4 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V103e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V104e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V105e3)~(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V106e4)~V102l\_27))))))))))){\unicdcdcdhd}(((p~(ap~\\
(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V107l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V108e1 \in A\_27a .  ({\unicdcdaddd} V109e2 \in A\_27a .  ({\unicdcdaddd} V110e3 \in \\
A\_27a .  ({\unicdcdaddd} V111e4 \in A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V108e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V109e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V110e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V111e4)~V107l\_27))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~V1x))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))){\unicdbdjded}({\unicdcdaddd} V112l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V113e1 \in \\
A\_27a .  ({\unicdcdaddd} V114e2 \in A\_27a .  ({\unicdcdaddd} V115e3 \in A\_27a .  ({\unicdcdaddd} V116e4 \in \\
A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V112l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V113e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V114e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V115e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V116e4)~V112l\_27)))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
V1x))){\unicdbdjded}({\unicdcdaddd} V117l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V118e1 \in \\
A\_27a .  ({\unicdcdaddd} V119e2 \in A\_27a .  ({\unicdcdaddd} V120e3 \in A\_27a .  ({\unicdcdaddd} V121e4 \in \\
A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V117l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V118e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V119e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V120e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V121e4)~V117l\_27)))))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))))~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V122l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  (\\
{\unicdcdaddd} V123e1 \in A\_27a .  ({\unicdcdaddd} V124e2 \in A\_27a .  ({\unicdcdaddd} V125e3 \in \\
A\_27a .  ({\unicdcdaddd} V126e4 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V122l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V123e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V124e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V125e3)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V126e4)~V122l\_27)))))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))))){\unicdbdjded}({\unicdcdaddd} V127l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V128e1 \in A\_27a .  ({\unicdcdaddd} V129e2 \in \\
A\_27a .  ({\unicdcdaddd} V130e3 \in A\_27a .  ({\unicdcdaddd} V131e4 \in A\_27a .  ((p~(ap~(\\
ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V127l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V128e1)~(ap~\\
(ap~(c\_2Elist\_2ECONS~A\_27a)~V129e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V130e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V131e4)~V127l\_27)))))))))))){\unicdcdcdhd}\\
((((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~V1x)){\unicdbdjded}({\unicdcdaddd} V132l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V133e1 \in A\_27a .  ({\unicdcdaddd} V134e2 \in A\_27a .  ({\unicdcdaddd} V135e3 \in \\
A\_27a .  ({\unicdcdaddd} V136e4 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V132l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V133e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V134e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V135e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V136e4)~V132l\_27)))))))))))){\unicdcdcdhd}\\
((((ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
V1x)=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V137l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V138e1 \in A\_27a .  ({\unicdcdaddd} V139e2 \in \\
A\_27a .  ({\unicdcdaddd} V140e3 \in A\_27a .  ({\unicdcdaddd} V141e4 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V137l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V138e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V139e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V140e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V141e4)~V137l\_27)))))))))))){\unicdcdcdhd}\\
((((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V142l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V143e1 \in A\_27a .  ({\unicdcdaddd} V144e2 \in \\
A\_27a .  ({\unicdcdaddd} V145e3 \in A\_27a .  ({\unicdcdaddd} V146e4 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V142l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V143e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V144e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V145e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V146e4)~V142l\_27)))))))))))){\unicdcdcdhd}\\
((((ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))=\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V147l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V148e1 \in A\_27a .  ({\unicdcdaddd} V149e2 \in A\_27a .  ({\unicdcdaddd} V150e3 \in \\
A\_27a .  ({\unicdcdaddd} V151e4 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V147l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V148e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V149e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V150e3)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V151e4)~V147l\_27)))))))))))){\unicdcdcdhd}\\
((((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}\\
({\unicdcdaddd} V152e1 \in A\_27a .  ({\unicdcdaddd} V153e2 \in A\_27a .  ({\unicdcdaddd} V154e3 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V152e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V153e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V154e3)~(c\_2Elist\_2ENIL~\\
A\_27a))))))))){\unicdcdcdhd}((((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))=(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V155e1 \in A\_27a .  ({\unicdcdaddd} V156e2 \in A\_27a .  (\\
{\unicdcdaddd} V157e3 \in A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V155e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V156e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V157e3)~(c\_2Elist\_2ENIL~A\_27a))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V158l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V159e1 \in A\_27a .  ({\unicdcdaddd} V160e2 \in A\_27a .  ({\unicdcdaddd} V161e3 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V159e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V160e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V161e3)~V158l\_27))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V162l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V163e1 \in A\_27a .  ({\unicdcdaddd} V164e2 \in A\_27a .  ({\unicdcdaddd} V165e3 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V163e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V164e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V165e3)~V162l\_27))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V166l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V167e1 \in A\_27a .  ({\unicdcdaddd} V168e2 \in A\_27a .  ({\unicdcdaddd} V169e3 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V167e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V168e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V169e3)~V166l\_27))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V170l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V171e1 \in A\_27a .  ({\unicdcdaddd} V172e2 \in \\
A\_27a .  ({\unicdcdaddd} V173e3 \in A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V171e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V172e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V173e3)~V170l\_27))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\\
\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
V1x))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V174l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V175e1 \in A\_27a .  ({\unicdcdaddd} V176e2 \in \\
A\_27a .  ({\unicdcdaddd} V177e3 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V174l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V175e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V176e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V177e3)~V174l\_27)))))))))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
V1x))){\unicdbdjded}({\unicdcdaddd} V178l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V179e1 \in \\
A\_27a .  ({\unicdcdaddd} V180e2 \in A\_27a .  ({\unicdcdaddd} V181e3 \in A\_27a .  ((p~(ap~(\\
ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V178l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V179e1)~(ap~\\
(ap~(c\_2Elist\_2ECONS~A\_27a)~V180e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V181e3)~V178l\_27)))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V182l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V183e1 \in A\_27a .  ({\unicdcdaddd} V184e2 \in A\_27a .  ({\unicdcdaddd} V185e3 \in \\
A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V182l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V183e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V184e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V185e3)~V182l\_27)))))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))))){\unicdbdjded}({\unicdcdaddd} V186l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V187e1 \in A\_27a .  ({\unicdcdaddd} V188e2 \in \\
A\_27a .  ({\unicdcdaddd} V189e3 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V186l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V187e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V188e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V189e3)~V186l\_27)))))))))){\unicdcdcdhd}\\
((((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~V1x)){\unicdbdjded}({\unicdcdaddd} V190l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V191e1 \in A\_27a .  ({\unicdcdaddd} V192e2 \in A\_27a .  ({\unicdcdaddd} V193e3 \in \\
A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V190l\_27)=V1x){\unicdcdcdhd}(V0l=\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V191e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V192e2)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V193e3)~V190l\_27)))))))))){\unicdcdcdhd}\\
((((ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))~\\
V1x)=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V194l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V195e1 \in A\_27a .  ({\unicdcdaddd} V196e2 \in \\
A\_27a .  ({\unicdcdaddd} V197e3 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V194l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V195e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V196e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V197e3)~V194l\_27)))))))))){\unicdcdcdhd}((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}\\
({\unicdcdaddd} V198l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V199e1 \in \\
A\_27a .  ({\unicdcdaddd} V200e2 \in A\_27a .  ({\unicdcdaddd} V201e3 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V198l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V199e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V200e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V201e3)~V198l\_27)))))))))){\unicdcdcdhd}((((ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))=(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V202l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V203e1 \in \\
A\_27a .  ({\unicdcdaddd} V204e2 \in A\_27a .  ({\unicdcdaddd} V205e3 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V202l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V203e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V204e2)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V205e3)~V202l\_27)))))))))){\unicdcdcdhd}((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO}))){\unicdbdjded}({\unicdcdaddd} V206e1 \in A\_27a .  ({\unicdcdaddd} V207e2 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V206e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V207e2)~(c\_2Elist\_2ENIL~A\_27a))))))){\unicdcdcdhd}((((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))=(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V208e1 \in A\_27a .  ({\unicdcdaddd} V209e2 \in A\_27a .  (\\
V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V208e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V209e2)~(c\_2Elist\_2ENIL~A\_27a))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V210l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V211e1 \in A\_27a .  ({\unicdcdaddd} V212e2 \in A\_27a .  (V0l=(\\
ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V211e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V212e2)~V210l\_27))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V213l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V214e1 \in A\_27a .  ({\unicdcdaddd} V215e2 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V214e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V215e2)~V213l\_27))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V216l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V217e1 \in A\_27a .  ({\unicdcdaddd} V218e2 \in A\_27a .  (V0l=(\\
ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V217e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V218e2)~V216l\_27))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V219l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V220e1 \in A\_27a .  ({\unicdcdaddd} V221e2 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V220e1)~(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V221e2)~V219l\_27))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\\
\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))~V1x))~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V222l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  (\\
{\unicdcdaddd} V223e1 \in A\_27a .  ({\unicdcdaddd} V224e2 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V222l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V223e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V224e2)~V222l\_27)))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))~\\
V1x))){\unicdbdjded}({\unicdcdaddd} V225l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V226e1 \in \\
A\_27a .  ({\unicdcdaddd} V227e2 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V225l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V226e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V227e2)~V225l\_27)))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO}))))~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V228l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  (\\
{\unicdcdaddd} V229e1 \in A\_27a .  ({\unicdcdaddd} V230e2 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V228l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V229e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~\\
V230e2)~V228l\_27)))))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V231l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V232e1 \in A\_27a .  ({\unicdcdaddd} V233e2 \in A\_27a .  ((p~(ap~\\
(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V231l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V232e1)~(ap~\\
(ap~(c\_2Elist\_2ECONS~A\_27a)~V233e2)~V231l\_27)))))))){\unicdcdcdhd}((((ap~\\
(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))~\\
V1x)){\unicdbdjded}({\unicdcdaddd} V234l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V235e1 \in \\
A\_27a .  ({\unicdcdaddd} V236e2 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V234l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V235e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V236e2)~V234l\_27)))))))){\unicdcdcdhd}(((\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\\
\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))~V1x)=(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V237l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V238e1 \in \\
A\_27a .  ({\unicdcdaddd} V239e2 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V237l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V238e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V239e2)~V237l\_27)))))))){\unicdcdcdhd}(((\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT2}~\\
\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V240l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V241e1 \in A\_27a .  ({\unicdcdaddd} V242e2 \in A\_27a .  (((ap~(\\
c\_2Elist\_2ELENGTH~A\_27a)~V240l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V241e1)~(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V242e2)~V240l\_27)))))))){\unicdcdcdhd}\\
((((ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT2}~\mname{c\_2Earithmetic\_2EZERO})))=(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V243l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V244e1 \in \\
A\_27a .  ({\unicdcdaddd} V245e2 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V243l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V244e1)~\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V245e2)~V243l\_27)))))))){\unicdcdcdhd}(((\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))){\unicdbdjded}({\unicdcdaddd} V246e1 \in \\
A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V246e1)~(c\_2Elist\_2ENIL~\\
A\_27a))))){\unicdcdcdhd}((((ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}\\
({\unicdcdaddd} V247e1 \in A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V247e1)~\\
(c\_2Elist\_2ENIL~A\_27a))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
\mname{c\_2Enum\_2E0})~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V248l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V249e1 \in A\_27a .  (V0l=(ap~(ap~\\
(c\_2Elist\_2ECONS~A\_27a)~V249e1)~V248l\_27))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~\mname{c\_2Enum\_2E0})){\unicdbdjded}({\unicdcdaddd} V250l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V251e1 \in A\_27a .  (V0l=(ap~(ap~\\
(c\_2Elist\_2ECONS~A\_27a)~V251e1)~V250l\_27))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V252l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V253e1 \in A\_27a .  (V0l=(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V253e1)~V252l\_27))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V254l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V255e1 \in A\_27a .  (V0l=(ap~(ap~\\
(c\_2Elist\_2ECONS~A\_27a)~V255e1)~V254l\_27))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\\
\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~V1x))~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}({\unicdcdaddd} V256l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  (\\
{\unicdcdaddd} V257e1 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V256l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~\\
A\_27a)~V257e1)~V256l\_27)))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~\\
V1x))){\unicdbdjded}({\unicdcdaddd} V258l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V259e1 \in \\
A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V258l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V259e1)~\\
V258l\_27)))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO}))))~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}\\
({\unicdcdaddd} V260l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V261e1 \in \\
A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~V1x)~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V260l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V261e1)~\\
V260l\_27)))))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))~(ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO}))))){\unicdbdjded}({\unicdcdaddd} V262l\_27 \in \\
(ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V263e1 \in A\_27a .  ((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
V1x)~(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V262l\_27))){\unicdcdcdhd}(V0l=(ap~(ap~(\\
c\_2Elist\_2ECONS~A\_27a)~V263e1)~V262l\_27)))))){\unicdcdcdhd}((((ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~V1x)){\unicdbdjded}(\\
{\unicdcdaddd} V264l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V265e1 \in \\
A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V264l\_27)=V1x){\unicdcdcdhd}(V0l=\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V265e1)~V264l\_27)))))){\unicdcdcdhd}((((ap~\\
(ap~c\_2Earithmetic\_2E\_2B~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO})))~V1x)=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V0l)){\unicdbdjded}({\unicdcdaddd} V266l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V267e1 \in \\
A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V266l\_27)=V1x){\unicdcdcdhd}(V0l=\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V267e1)~V266l\_27)))))){\unicdcdcdhd}((((ap~\\
(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=(ap~(ap~c\_2Earithmetic\_2E\_2B~\\
V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\\
\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}({\unicdcdaddd} V268l\_27 \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ({\unicdcdaddd} V269e1 \in A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~\\
V268l\_27)=V1x){\unicdcdcdhd}(V0l=(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V269e1)~\\
V268l\_27)))))){\unicdcdcdhd}((((ap~(ap~c\_2Earithmetic\_2E\_2B~V1x)~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))=(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l)){\unicdbdjded}({\unicdcdaddd} V270l\_27 \in (ty\_2Elist\_2Elist~A\_27a) .  ({\unicdcdaddd} V271e1 \in \\
A\_27a .  (((ap~(c\_2Elist\_2ELENGTH~A\_27a)~V270l\_27)=V1x){\unicdcdcdhd}(V0l=\\
(ap~(ap~(c\_2Elist\_2ECONS~A\_27a)~V271e1)~V270l\_27)))))){\unicdcdcdhd}((((ap~\\
(c\_2Elist\_2ELENGTH~A\_27a)~V0l)=\mname{c\_2Enum\_2E0}){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~\\
A\_27a))){\unicdcdcdhd}(((\mname{c\_2Enum\_2E0}=(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l)){\unicdbdjded}\\
(V0l=(c\_2Elist\_2ENIL~A\_27a))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Eprim\_\_rec\_2E\_3C}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~(ap~\mname{c\_2Earithmetic\_2ENUMERAL}~\\
(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))){\unicdbdjded}(V0l=\\
(c\_2Elist\_2ENIL~A\_27a))){\unicdcdcdhd}(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E}~(\\
ap~\mname{c\_2Earithmetic\_2ENUMERAL}~(ap~\mname{c\_2Earithmetic\_2EBIT1}~\mname{c\_2Earithmetic\_2EZERO})))~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~A\_27a))){\unicdcdcdhd}\\
(((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3E\_3D}~\mname{c\_2Enum\_2E0})~(ap~(c\_2Elist\_2ELENGTH~\\
A\_27a)~V0l))){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~A\_27a))){\unicdcdcdhd}((p~(ap~(ap~\mname{c\_2Earithmetic\_2E\_3C\_3D}~\\
(ap~(c\_2Elist\_2ELENGTH~A\_27a)~V0l))~\mname{c\_2Enum\_2E0})){\unicdbdjded}(V0l=(c\_2Elist\_2ENIL~\\
A\_27a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
