\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\uniddcgcg{\lambda}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{thm\_2EASCIInumbers\_2EtoString\_\_inj (TMZtvvH7GGBi19szub5KepMmo3Fg4y23sfX)}
\maketitle
Let $ ty\_2Estring\_2Echar : {\iota}$ be given.
Assume the following.
\begin{equation}
{{nonempty}~{ty\_2Estring\_2Echar}}\label{hyp:ogfgpfehjhpfcdfedhehchjgoghgpfcdfedgigbgch}
\end{equation}
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\_2Ebool\_2EARB : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} A\_27a .  {{{nonempty}~{A\_27a}}{\unicdbdjdcd}{{{c\_2Ebool\_2EARB}~{A\_27a}} \in {A\_27a}}}}\label{hyp:ngfgngpfdgpfcdfecgpgpgmgpfcdfebecfce}
\end{equation}
Let $ c\_2Enum\_2EZERO\_\_REP : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Enum\_2EZERO\_\_REP} \in {omega}}\label{hyp:ngfgngpfdgpfcdfeogfhngpfcdfekffecfpepfpfcffeaf}
\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\_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:dgpfcdfeogfhngpfcdfead}
We define $\mname{c\_2Enum\_2E0}$ to be ${({{{ap}~{c\_2Enum\_2EABS\_\_num}}~{c\_2Enum\_2EZERO\_\_REP}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebgchjgehigngfgehjgdgpfcdfekffecfpe}
We define $\mname{c\_2Earithmetic\_2EZERO}$ to be ${\mname{c\_2Enum\_2E0}}$.
\end{definition}
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}
\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}
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: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: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:dgpfcdfebgchjgehigngfgehjgdgpfcdfeoeffnefecfbeme}
We define $\mname{c\_2Earithmetic\_2ENUMERAL}$ to be ${{\uniddcgcg} V0x \in {ty\_2Enum\_2Enum} .  {V0x}}$.
\end{definition}
Let $ c\_2Estring\_2ECHR : {\iota}$ be given.
Assume the following.
\begin{equation}
{{c\_2Estring\_2ECHR} \in {({{ty\_2Estring\_2Echar}^{{ty\_2Enum\_2Enum}}})}}\label{hyp:ngfgngpfdgpfcdfedhehchjgoghgpfcdfedeiecf}
\end{equation}
\begin{definition}\label{def:dgpfcdfedgpgngcgjgogpfcdfele}
We define $\mname{c\_2Ecombin\_2EK}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {({{\uniddcgcg} V0x \in {A\_27a} .  {({{\uniddcgcg} V1y \in {A\_27b} .  {V0x}})}})}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfedgpgngcgjgogpfcdfedf}
We define $\mname{c\_2Ecombin\_2ES}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {{\uniddcgcg} A\_27c : {\iota} .  {({{\uniddcgcg} V0f \in {({{({{A\_27c}^{{A\_27b}}})}^{{A\_27a}}})} .  {({{\uniddcgcg} V1g \in {({{A\_27b}^{{A\_27a}}})} .  {({{\uniddcgcg} V2x \in {A\_27a} .  {({{{ap}~{({{{ap}~{V0f}}~{V2x}})}}~{({{{ap}~{V1g}}~{V2x}})}})}})}})}})}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfedgpgngcgjgogpfcdfeje}
We define $\mname{c\_2Ecombin\_2EI}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {({{{ap}~{({{{ap}~{({{{{\mname{c\_2Ecombin\_2ES}}~{A\_27a}}~{({{A\_27a}^{{A\_27a}}})}}~{A\_27a}})}}~{({{{\mname{c\_2Ecombin\_2EK}}~{A\_27a}}~{({{A\_27a}^{{A\_27a}}})}})}})}}~{({{{\mname{c\_2Ecombin\_2EK}}~{A\_27a}}~{A\_27a}})}})}}$.
\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: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}
\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: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}
\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:dgpfcdfecgpgpgmgpfcdfemgjgehfgchbgmgpfpfdgbgdhfg}
We define $\mname{c\_2Ebool\_2Eliteral\_\_case}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {({{\uniddcgcg} V0f \in {({{A\_27b}^{{A\_27a}}})} .  {({{\uniddcgcg} V1x \in {A\_27a} .  {({{{ap}~{V0f}}~{V1x}})}})}})}}}$.
\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}
\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:dgpfcdfechfgmgbgehjgpgogpfcdfehfge}
We define $\mname{c\_2Erelation\_2EWF}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} V0R \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{({{2}^{{A\_27a}}})}})}}~{({{\uniddcgcg} V1B \in {({{2}^{{A\_27a}}})} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{\mname{c\_2Ebool\_2E\_3F}}~{A\_27a}})}}~{({{\uniddcgcg} V2w \in {A\_27a} .  {({{{ap}~{V1B}}~{V2w}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ebool\_2E\_3F}}~{A\_27a}})}}~{({{\uniddcgcg} V3min \in {A\_27a} .  {({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_2F\_5C}}}~{({{{ap}~{V1B}}~{V3min}})}})}}~{({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{A\_27a}})}}~{({{\uniddcgcg} V4b \in {A\_27a} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{V0R}}~{V4b}})}}~{V3min}})}})}}~{({{{ap}~{\mname{c\_2Ebool\_2E\_7E}}}~{({{{ap}~{V1B}}~{V4b}})}})}})}})}})}})}})}})}})}})}})}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfechfgmgbgehjgpgogpfcdfecffedfefcfjedeef}
We define $\mname{c\_2Erelation\_2ERESTRICT}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {{\uniddcgcg} V0f \in {({{A\_27b}^{{A\_27a}}})} .  {{\uniddcgcg} V1R \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {{\uniddcgcg} V2x \in {A\_27a} .  {({{\uniddcgcg} V3y \in {A\_27a} .  {({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{A\_27b}})}}~{({{{ap}~{({{{ap}~{V1R}}~{V3y}})}}~{V2x}})}})}}~{({{{ap}~{V0f}}~{V3y}})}})}}~{({{c\_2Ebool\_2EARB}~{A\_27b}})}})}})}}}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfechfgmgbgehjgpgogpfcdfeefde}
We define $\mname{c\_2Erelation\_2ETC}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} V0R \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {{\uniddcgcg} V1a \in {A\_27a} .  {{\uniddcgcg} V2b \in {A\_27a} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{({{({{2}^{{A\_27a}}})}^{{A\_27a}}})}})}}~{({{\uniddcgcg} V3P \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_2F\_5C}}}~{({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{A\_27a}})}}~{({{\uniddcgcg} V4x \in {A\_27a} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{A\_27a}})}}~{({{\uniddcgcg} V5y \in {A\_27a} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{V0R}}~{V4x}})}}~{V5y}})}})}}~{({{{ap}~{({{{ap}~{V3P}}~{V4x}})}}~{V5y}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{A\_27a}})}}~{({{\uniddcgcg} V6x \in {A\_27a} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{A\_27a}})}}~{({{\uniddcgcg} V7y \in {A\_27a} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{A\_27a}})}}~{({{\uniddcgcg} V8z \in {A\_27a} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Ebool\_2E\_2F\_5C}}}~{({{{ap}~{({{{ap}~{V3P}}~{V6x}})}}~{V7y}})}})}}~{({{{ap}~{({{{ap}~{V3P}}~{V7y}})}}~{V8z}})}})}})}}~{({{{ap}~{({{{ap}~{V3P}}~{V6x}})}}~{V8z}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{V3P}}~{V1a}})}}~{V2b}})}})}})}})}}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfechfgmgbgehjgpgogpfcdfebgahahchpgih}
We define $\mname{c\_2Erelation\_2Eapprox}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {{\uniddcgcg} V0R \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {{\uniddcgcg} V1M \in {({{({{A\_27b}^{{A\_27a}}})}^{{({{A\_27b}^{{A\_27a}}})}}})} .  {{\uniddcgcg} V2x \in {A\_27a} .  {{\uniddcgcg} V3f \in {({{A\_27b}^{{A\_27a}}})} .  {({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{({{A\_27b}^{{A\_27a}}})}})}}~{V3f}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2ERESTRICT}}~{A\_27a}}~{A\_27b}})}}~{({{\uniddcgcg} V4y \in {A\_27a} .  {({{{ap}~{({{{ap}~{V1M}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2ERESTRICT}}~{A\_27a}}~{A\_27b}})}}~{V3f}})}}~{V0R}})}}~{V4y}})}})}}~{V4y}})}})}})}}~{V0R}})}}~{V2x}})}})}}}}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfechfgmgbgehjgpgogpfcdfeehigfgpfpfggfhog}
We define $\mname{c\_2Erelation\_2Ethe\_\_fun}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {{\uniddcgcg} V0R \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {{\uniddcgcg} V1M \in {({{({{A\_27b}^{{A\_27a}}})}^{{({{A\_27b}^{{A\_27a}}})}}})} .  {{\uniddcgcg} V2x \in {A\_27a} .  {({{{ap}~{({{\mname{c\_2Emin\_2E\_40}}~{({{A\_27b}^{{A\_27a}}})}})}}~{({{\uniddcgcg} V3f \in {({{A\_27b}^{{A\_27a}}})} .  {({{{ap}~{({{{ap}~{({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2Eapprox}}~{A\_27a}}~{A\_27b}})}}~{V0R}})}}~{V1M}})}}~{V2x}})}}~{V3f}})}})}})}}}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfechfgmgbgehjgpgogpfcdfehfgecffede}
We define $\mname{c\_2Erelation\_2EWFREC}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {{\uniddcgcg} V0R \in {({{({{2}^{{A\_27a}}})}^{{A\_27a}}})} .  {{\uniddcgcg} V1M \in {({{({{A\_27b}^{{A\_27a}}})}^{{({{A\_27b}^{{A\_27a}}})}}})} .  {({{\uniddcgcg} V2x \in {A\_27a} .  {({{{ap}~{({{{ap}~{V1M}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2ERESTRICT}}~{A\_27a}}~{A\_27b}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2Ethe\_\_fun}}~{A\_27a}}~{A\_27b}})}}~{({{{ap}~{({{\mname{c\_2Erelation\_2ETC}}~{A\_27a}})}}~{V0R}})}})}}~{({{\uniddcgcg} V3f \in {({{A\_27b}^{{A\_27a}}})} .  {({{\uniddcgcg} V4v \in {A\_27a} .  {({{{ap}~{({{{ap}~{V1M}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2ERESTRICT}}~{A\_27a}}~{A\_27b}})}}~{V3f}})}}~{V0R}})}}~{V4v}})}})}}~{V4v}})}})}})}})}}~{V2x}})}})}}~{V0R}})}}~{V2x}})}})}}~{V2x}})}})}}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebedfdejejeogfhngcgfgchdhpfcdfeiefeif}
We define $\mname{c\_2EASCIInumbers\_2EHEX}$ to be ${({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2EWFREC}}~{ty\_2Enum\_2Enum}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_40}}~{({{({{2}^{{ty\_2Enum\_2Enum}}})}^{{ty\_2Enum\_2Enum}}})}})}}~{({{\uniddcgcg} V0R \in {({{({{2}^{{ty\_2Enum\_2Enum}}})}^{{ty\_2Enum\_2Enum}}})} .  {({{{ap}~{({{\mname{c\_2Erelation\_2EWF}}~{ty\_2Enum\_2Enum}})}}~{V0R}})}})}})}})}}~{({{\uniddcgcg} V1HEX \in {({{ty\_2Estring\_2Echar}^{{ty\_2Enum\_2Enum}}})} .  {({{\uniddcgcg} V2a \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{({{{\mname{c\_2Ebool\_2Eliteral\_\_case}}~{ty\_2Enum\_2Enum}}~{ty\_2Estring\_2Echar}})}}~{({{\uniddcgcg} V3v \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{\mname{c\_2Enum\_2E0}}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Enum\_2Enum}})}}~{V3v}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{c\_2Ebool\_2EARB}~{ty\_2Estring\_2Echar}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}}~{V2a}})}})}})}})}$.
\end{definition}
Let $ c\_2Enumposrep\_2En2l : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Enumposrep\_2En2l \in (((ty\_2Elist\_2Elist~ty\_2Enum\_2Enum)^{{ty\_2Enum\_2Enum}})^{{ty\_2Enum\_2Enum}})\end{array}
\label{hyp:ngfgngpfdgpfcdfeogfhngahpgdhchfgahpfcdfeogcdmg}
\end{equation}
Let $ c\_2Elist\_2EMAP : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}{\unicdcdadad} A\_27b .  nonempty~A\_27b{\unicdbdjdcd}c\_2Elist\_2EMAP~\\
A\_27a~A\_27b \in (((ty\_2Elist\_2Elist~A\_27b)^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})^{{({{A\_27b}^{{A\_27a}}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfenebeaf}
\end{equation}
Let $ c\_2Elist\_2EREVERSE : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}c\_2Elist\_2EREVERSE~A\_27a \in ((ty\_2Elist\_2Elist~\\
A\_27a)^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfecffegffecfdffe}
\end{equation}
\begin{definition}\label{def:dgpfcdfebedfdejejeogfhngcgfgchdhpfcdfeogcddh}
We define $\mname{c\_2EASCIInumbers\_2En2s}$ to be ${{\uniddcgcg} V0b \in {ty\_2Enum\_2Enum} .  {{\uniddcgcg} V1f \in {({{ty\_2Estring\_2Echar}^{{ty\_2Enum\_2Enum}}})} .  {{\uniddcgcg} V2n \in {ty\_2Enum\_2Enum} .  {({{{ap}~{({{c\_2Elist\_2EREVERSE}~{ty\_2Estring\_2Echar}})}}~{({{{ap}~{({{{ap}~{({{{c\_2Elist\_2EMAP}~{ty\_2Enum\_2Enum}}~{ty\_2Estring\_2Echar}})}}~{V1f}})}}~{({{{ap}~{({{{ap}~{c\_2Enumposrep\_2En2l}}~{V0b}})}}~{V2n}})}})}})}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebedfdejejeogfhngcgfgchdhpfcdfeogfhngpfpfehpgpfpfegfgdgpfpfdhehchjgoghg}
We define $\mname{c\_2EASCIInumbers\_2Enum\_\_to\_\_dec\_\_string}$ to be ${({{{ap}~{({{{ap}~{\mname{c\_2EASCIInumbers\_2En2s}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{\mname{c\_2EASCIInumbers\_2EHEX}}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebedfdejejeogfhngcgfgchdhpfcdfeffoeiefeif}
We define $\mname{c\_2EASCIInumbers\_2EUNHEX}$ to be ${({{{ap}~{({{{ap}~{({{{\mname{c\_2Erelation\_2EWFREC}}~{ty\_2Estring\_2Echar}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_40}}~{({{({{2}^{{ty\_2Estring\_2Echar}}})}^{{ty\_2Estring\_2Echar}}})}})}}~{({{\uniddcgcg} V0R \in {({{({{2}^{{ty\_2Estring\_2Echar}}})}^{{ty\_2Estring\_2Echar}}})} .  {({{{ap}~{({{\mname{c\_2Erelation\_2EWF}}~{ty\_2Estring\_2Echar}})}}~{V0R}})}})}})}})}}~{({{\uniddcgcg} V1UNHEX \in {({{ty\_2Enum\_2Enum}^{{ty\_2Estring\_2Echar}}})} .  {({{\uniddcgcg} V2a \in {ty\_2Estring\_2Echar} .  {({{{ap}~{({{{ap}~{({{{\mname{c\_2Ebool\_2Eliteral\_\_case}}~{ty\_2Estring\_2Echar}}~{ty\_2Enum\_2Enum}})}}~{({{\uniddcgcg} V3v \in {ty\_2Estring\_2Echar} .  {({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{\mname{c\_2Enum\_2E0}}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}}~{({{{ap}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Ebool\_2ECOND}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{ty\_2Estring\_2Echar}})}}~{V3v}})}}~{({{{ap}~{c\_2Estring\_2ECHR}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}})}})}})}}~{({{{ap}~{({{\mname{c\_2Ecombin\_2EI}}~{ty\_2Enum\_2Enum}})}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}})}})}}~{({{c\_2Ebool\_2EARB}~{ty\_2Enum\_2Enum}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}})}}~{V2a}})}})}})}})}$.
\end{definition}
Let $ c\_2Enumposrep\_2El2n : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Enumposrep\_2El2n \in ((ty\_2Enum\_2Enum^{{({{ty\_2Elist\_2Elist}~{ty\_2Enum\_2Enum}})}})^{{ty\_2Enum\_2Enum}})\end{array}
\label{hyp:ngfgngpfdgpfcdfeogfhngahpgdhchfgahpfcdfemgcdog}
\end{equation}
\begin{definition}\label{def:dgpfcdfebedfdejejeogfhngcgfgchdhpfcdfedhcdog}
We define $\mname{c\_2EASCIInumbers\_2Es2n}$ to be ${{\uniddcgcg} V0b \in {ty\_2Enum\_2Enum} .  {{\uniddcgcg} V1f \in {({{ty\_2Enum\_2Enum}^{{ty\_2Estring\_2Echar}}})} .  {{\uniddcgcg} V2s \in {({{ty\_2Elist\_2Elist}~{ty\_2Estring\_2Echar}})} .  {({{{ap}~{({{{ap}~{c\_2Enumposrep\_2El2n}}~{V0b}})}}~{({{{ap}~{({{{ap}~{({{{c\_2Elist\_2EMAP}~{ty\_2Estring\_2Echar}}~{ty\_2Enum\_2Enum}})}}~{V1f}})}}~{({{{ap}~{({{c\_2Elist\_2EREVERSE}~{ty\_2Estring\_2Echar}})}}~{V2s}})}})}})}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfebedfdejejeogfhngcgfgchdhpfcdfeogfhngpfpfggchpgngpfpfegfgdgpfpfdhehchjgoghg}
We define $\mname{c\_2EASCIInumbers\_2Enum\_\_from\_\_dec\_\_string}$ to be ${({{{ap}~{({{{ap}~{\mname{c\_2EASCIInumbers\_2Es2n}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2ENUMERAL}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT2}}}~{({{{ap}~{\mname{c\_2Earithmetic\_2EBIT1}}}~{\mname{c\_2Earithmetic\_2EZERO}}})}})}})}})}})}}~{\mname{c\_2EASCIInumbers\_2EUNHEX}}})}$.
\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}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ((ap~\mname{c\_2EASCIInumbers\_2Enum\_\_from\_\_dec\_\_string}~\\
(ap~\mname{c\_2EASCIInumbers\_2Enum\_\_to\_\_dec\_\_string}~V0n))=V0n))\end{array}
\label{hyp:ehigngpfcdfebedfdejejeogfhngcgfgchdhpfcdfeehpgoefhngpfpfehpgdfehchjgoghg}
\end{equation}
Assume the following.
\begin{equation}
{True}\label{hyp:ehigngpfcdfecgpgpgmgpfcdfeefcfffefie}
\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} V0t \in 2 .  (((True{\unicdbdjdcd}(p~V0t)){\unicdbdjded}(p~V0t)){\unicdcdcdhd}((((p~V0t){\unicdbdjdcd}True){\unicdbdjded}\\
True){\unicdcdcdhd}(((False{\unicdbdjdcd}(p~V0t)){\unicdbdjded}True){\unicdcdcdhd}((((p~V0t){\unicdbdjdcd}(p~V0t)){\unicdbdjded}True){\unicdcdcdhd}((\\
(p~V0t){\unicdbdjdcd}False){\unicdbdjded}(\preoh (p~V0t))))))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfejeneafpfpfdemebeffdffedf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(({\unicdcdadad} V0t \in 2 .  ((\preoh (\preoh (p~V0t))){\unicdbdjded}(p~V0t))){\unicdcdcdhd}(((\preoh True){\unicdbdjded}False){\unicdcdcdhd}\\
((\preoh False){\unicdbdjded}True)))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfeoepeefpfpfdemebeffdffedf}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} A\_27a .  {{{nonempty}~{A\_27a}}{\unicdbdjdcd}{({{\unicdcdadad} V0x \in {A\_27a} .  {({{V0x}={V0x}})}})}}}\label{hyp:ehigngpfcdfecgpgpgmgpfcdfefebfpfpfcffegeme}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0t \in 2 .  (((True{\unicdbdjded}(p~V0t)){\unicdbdjded}(p~V0t)){\unicdcdcdhd}((((p~V0t){\unicdbdjded}True){\unicdbdjded}\\
(p~V0t)){\unicdcdcdhd}(((False{\unicdbdjded}(p~V0t)){\unicdbdjded}(\preoh (p~V0t))){\unicdcdcdhd}(((p~V0t){\unicdbdjded}False){\unicdbdjded}(\preoh (\\
p~V0t)))))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfefebfpfpfdemebeffdffedf}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0t \in {2} .  {({{({\preoh{{({\preoh{{({{p}~{V0t}})}}})}}})}{\unicdbdjded}{({{p}~{V0t}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfeoepeefpfpfoepeef}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0A \in {2} .  {({{({{p}~{V0A}})}{\unicdbdjdcd}{({{({\preoh{{({{p}~{V0A}})}}})}{\unicdbdjdcd}{False}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfebeoeeepfpfjeoegfpfpfjeneaf}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0A \in 2 .  ({\unicdcdadad} V1B \in 2 .  (((\preoh ((p~V0A){\unicdcdcdid}(p~V1B))){\unicdbdjdcd}False){\unicdbdjded}\\
(((p~V0A){\unicdbdjdcd}False){\unicdbdjdcd}((\preoh (p~V1B)){\unicdbdjdcd}False)))))\end{array}
\label{hyp:ehigngpfcdfedhbgehpfcdfepecfpfpfeeffbemecd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0A \in 2 .  ({\unicdcdadad} V1B \in 2 .  (((\preoh ((\preoh (p~V0A)){\unicdcdcdid}(p~V1B))){\unicdbdjdcd}False){\unicdbdjded}\\
((p~V0A){\unicdbdjdcd}((\preoh (p~V1B)){\unicdbdjdcd}False)))))\end{array}
\label{hyp:ehigngpfcdfedhbgehpfcdfepecfpfpfeeffbemedd}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0A \in {2} .  {({{({{({\preoh{{({{p}~{V0A}})}}})}{\unicdbdjdcd}{False}})}{\unicdbdjdcd}{({{({{({{p}~{V0A}})}{\unicdbdjdcd}{False}})}{\unicdbdjdcd}{False}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfebeoeeepfpfjeoegfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0p \in 2 .  ({\unicdcdadad} V1q \in 2 .  ({\unicdcdadad} V2r \in 2 .  (((p~V0p){\unicdbdjded}(\\
(p~V1q){\unicdbdjded}(p~V2r))){\unicdbdjded}(((p~V0p){\unicdcdcdid}((p~V1q){\unicdcdcdid}(p~V2r))){\unicdcdcdhd}(((p~V0p){\unicdcdcdid}((\preoh (\\
p~V2r)){\unicdcdcdid}(\preoh (p~V1q)))){\unicdcdcdhd}(((p~V1q){\unicdcdcdid}((\preoh (p~V2r)){\unicdcdcdid}(\preoh (p~V0p)))){\unicdcdcdhd}((p~V2r){\unicdcdcdid}\\
((\preoh (p~V1q)){\unicdcdcdid}(\preoh (p~V0p)))))))))))\end{array}
\label{hyp:ehigngpfcdfedhbgehpfcdfeegdgpfpffgbh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0p \in 2 .  ({\unicdcdadad} V1q \in 2 .  ({\unicdcdadad} V2r \in 2 .  (((p~V0p){\unicdbdjded}(\\
(p~V1q){\unicdbdjdcd}(p~V2r))){\unicdbdjded}(((p~V0p){\unicdcdcdid}(p~V1q)){\unicdcdcdhd}(((p~V0p){\unicdcdcdid}(\preoh (p~V2r))){\unicdcdcdhd}((\\
\preoh (p~V1q)){\unicdcdcdid}((p~V2r){\unicdcdcdid}(\preoh (p~V0p))))))))))\end{array}
\label{hyp:ehigngpfcdfedhbgehpfcdfeegdgpfpfjgngah}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0p \in {2} .  {({{\unicdcdadad} V1q \in {2} .  {({{({\preoh{{({{({{p}~{V0p}})}{\unicdbdjdcd}{({{p}~{V1q}})}})}}})}{\unicdbdjdcd}{({{p}~{V0p}})}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfeahehigpfpfogjgbd}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0p \in {2} .  {({{\unicdcdadad} V1q \in {2} .  {({{({\preoh{{({{({{p}~{V0p}})}{\unicdbdjdcd}{({{p}~{V1q}})}})}}})}{\unicdbdjdcd}{({\preoh{{({{p}~{V1q}})}}})}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfeahehigpfpfogjgcd}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0p \in {2} .  {({{\unicdcdadad} V1q \in {2} .  {({{({\preoh{{({{({{p}~{V0p}})}{\unicdcdcdid}{({{p}~{V1q}})}})}}})}{\unicdbdjdcd}{({\preoh{{({{p}~{V0p}})}}})}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfeahehigpfpfogpgbd}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0p \in {2} .  {({{\unicdcdadad} V1q \in {2} .  {({{({\preoh{{({{({{p}~{V0p}})}{\unicdcdcdid}{({{p}~{V1q}})}})}}})}{\unicdbdjdcd}{({\preoh{{({{p}~{V1q}})}}})}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfeahehigpfpfogpgcd}
\end{equation}
Assume the following.
\begin{equation}
{({{\unicdcdadad} V0p \in {2} .  {({{({\preoh{{({\preoh{{({{p}~{V0p}})}}})}}})}{\unicdbdjdcd}{({{p}~{V0p}})}})}})}\label{hyp:ehigngpfcdfedhbgehpfcdfeahehigpfpfogog}
\end{equation}
\begin{theorem}\label{thm:ehigngpfcdfebedfdejejeogfhngcgfgchdhpfcdfeehpgdfehchjgoghgpfpfjgogkg}
$$\begin{array}{c}({\unicdcdadad} V0n \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1m \in ty\_2Enum\_2Enum .  (\\
((ap~\mname{c\_2EASCIInumbers\_2Enum\_\_to\_\_dec\_\_string}~V0n)=(ap~\mname{c\_2EASCIInumbers\_2Enum\_\_to\_\_dec\_\_string}~\\
V1m)){\unicdbdjded}(V0n=V1m))))\end{array}$$
\end{theorem}
\end{document}
