\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\_2Erich\_\_list\_2EFOLDL\_\_REVERSE (TMdrMwZZQDpAVZBpGoB6zRKfuGbVgcJ1ecL)}
\maketitle
\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}
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\_2EFOLDR : {{\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\_2EFOLDR~\\
A\_27a~A\_27b \in (((A\_27b^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})^{{A\_27b}})^{{({{({{A\_27b}^{{A\_27b}}})}^{{A\_27a}}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfegepemeeecf}
\end{equation}
Let $ c\_2Elist\_2EFOLDL : {{\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\_2EFOLDL~\\
A\_27a~A\_27b \in (((A\_27b^{{({{ty\_2Elist\_2Elist}~{A\_27a}})}})^{{A\_27b}})^{{({{({{A\_27b}^{{A\_27a}}})}^{{A\_27b}}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfemgjgdhehpfcdfegepemeeeme}
\end{equation}
\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}
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} V0t \in 2 .  (({\unicdcdadad} V1x \in \\
A\_27a .  (p~V0t)){\unicdbdjded}(p~V0t)))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfegepecfbememepfpfdfjeneaf}
\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} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0l \in (ty\_2Elist\_2Elist~\\
A\_27a) .  ((ap~(c\_2Elist\_2EREVERSE~A\_27a)~(ap~(c\_2Elist\_2EREVERSE~\\
A\_27a)~V0l))=V0l))\end{array}
\label{hyp:ehigngpfcdfemgjgdhehpfcdfecffegffecfdffepfpfcffegffecfdffe}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}{\unicdcdadad} A\_27b .  nonempty~A\_27b{\unicdbdjdcd}(\\
{\unicdcdadad} V0f \in ((A\_27a^{{A\_27b}})^{{A\_27a}}) .  ({\unicdcdadad} V1e \in A\_27a .  ({\unicdcdadad} V2l \in \\
(ty\_2Elist\_2Elist~A\_27b) .  ((ap~(ap~(ap~(c\_2Elist\_2EFOLDL~A\_27b~\\
A\_27a)~V0f)~V1e)~V2l)=(ap~(ap~(ap~(c\_2Elist\_2EFOLDR~A\_27b~A\_27a)~\\
({\uniddcgcg} V3x \in A\_27b .  ({\uniddcgcg} V4y \in A\_27a .  (ap~(ap~V0f~V4y)~V3x))))~V1e)~(\\
ap~(c\_2Elist\_2EREVERSE~A\_27b)~V2l))))))\end{array}
\label{hyp:ehigngpfcdfechjgdgigpfpfmgjgdhehpfcdfegepemeeemepfpfgepemeeecfpfpfcffegffecfdffe}
\end{equation}
\begin{theorem}\label{thm:ehigngpfcdfechjgdgigpfpfmgjgdhehpfcdfegepemeeemepfpfcffegffecfdffe}
$$\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}{\unicdcdadad} A\_27b .  nonempty~A\_27b{\unicdbdjdcd}(\\
{\unicdcdadad} V0f \in ((A\_27a^{{A\_27b}})^{{A\_27a}}) .  ({\unicdcdadad} V1e \in A\_27a .  ({\unicdcdadad} V2l \in \\
(ty\_2Elist\_2Elist~A\_27b) .  ((ap~(ap~(ap~(c\_2Elist\_2EFOLDL~A\_27b~\\
A\_27a)~V0f)~V1e)~(ap~(c\_2Elist\_2EREVERSE~A\_27b)~V2l))=(ap~(ap~(\\
ap~(c\_2Elist\_2EFOLDR~A\_27b~A\_27a)~({\uniddcgcg} V3x \in A\_27b .  ({\uniddcgcg} V4y \in A\_27a .  \\
(ap~(ap~V0f~V4y)~V3x))))~V1e)~V2l)))))\end{array}$$
\end{theorem}
\end{document}
