\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{thm\_2EASCIInumbers\_2Es2n\_\_compute (TMTVYvFaSXVAXjBTZMdBWSADmWd7tBWEqrj)}
\maketitle
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\_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}
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 $ ty\_2Enum\_2Enum : {\iota}$ be given.
Assume the following.
\begin{equation}
{{nonempty}~{ty\_2Enum\_2Enum}}\label{hyp:ogfgpfehjhpfcdfeogfhngpfcdfeogfhng}
\end{equation}
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}
Let $ ty\_2Estring\_2Echar : {\iota}$ be given.
Assume the following.
\begin{equation}
{{nonempty}~{ty\_2Estring\_2Echar}}\label{hyp:ogfgpfehjhpfcdfedhehchjgoghgpfcdfedgigbgch}
\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: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}
Let $ c\_2Estring\_2EIMPLODE : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Estring\_2EIMPLODE \in ((ty\_2Elist\_2Elist~ty\_2Estring\_2Echar)^{{({{ty\_2Elist\_2Elist}~{ty\_2Estring\_2Echar}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfedhehchjgoghgpfcdfejeneafmepeeefe}
\end{equation}
Let $ c\_2Estring\_2EEXPLODE : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}c\_2Estring\_2EEXPLODE \in ((ty\_2Elist\_2Elist~ty\_2Estring\_2Echar)^{{({{ty\_2Elist\_2Elist}~{ty\_2Estring\_2Echar}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfedhehchjgoghgpfcdfefeifafmepeeefe}
\end{equation}
\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}
Assume the following.
\begin{equation}
{True}\label{hyp:ehigngpfcdfecgpgpgmgpfcdfeefcfffefie}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0x \in A\_27a .  ((V0x=V0x){\unicdbdjded}\\
True))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfecffegemepfpfdemebeffdffe}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} V0s \in (ty\_2Elist\_2Elist~ty\_2Estring\_2Echar) .  (((ap~c\_2Estring\_2EEXPLODE~\\
V0s)=V0s){\unicdcdcdhd}((ap~c\_2Estring\_2EIMPLODE~V0s)=V0s)))\end{array}
\label{hyp:ehigngpfcdfedhehchjgoghgpfcdfejeneafmepeeefepfpffeifafmepeeefepfpfje}
\end{equation}
\begin{theorem}\label{thm:ehigngpfcdfebedfdejejeogfhngcgfgchdhpfcdfedhcdogpfpfdgpgngahfhehfg}
$$\begin{array}{c}({\unicdcdadad} V0b \in ty\_2Enum\_2Enum .  ({\unicdcdadad} V1f \in (ty\_2Enum\_2Enum^{{ty\_2Estring\_2Echar}}) .  \\
({\unicdcdadad} V2s \in (ty\_2Elist\_2Elist~ty\_2Estring\_2Echar) .  ((ap~(ap~\\
(ap~\mname{c\_2EASCIInumbers\_2Es2n}~V0b)~V1f)~V2s)=(ap~(ap~c\_2Enumposrep\_2El2n~\\
V0b)~(ap~(ap~(c\_2Elist\_2EMAP~ty\_2Estring\_2Echar~ty\_2Enum\_2Enum)~\\
V1f)~(ap~(c\_2Elist\_2EREVERSE~ty\_2Estring\_2Echar)~(ap~c\_2Estring\_2EEXPLODE~\\
V2s))))))))\end{array}$$
\end{theorem}
\end{document}
