\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{thm\_2Erelation\_2EINVOL (TMTUHgUNdYgztLhRijAs7HhkoPk8c72xdik)}
\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}
\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: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:dgpfcdfedgpgngcgjgogpfcdfepg}
We define $\mname{c\_2Ecombin\_2Eo}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {{\uniddcgcg} A\_27c : {\iota} .  {{\uniddcgcg} V0f \in {({{A\_27b}^{{A\_27c}}})} .  {{\uniddcgcg} V1g \in {({{A\_27c}^{{A\_27a}}})} .  {({{\uniddcgcg} V2x \in {A\_27a} .  {({{{ap}~{V0f}}~{({{{ap}~{V1g}}~{V2x}})}})}})}}}}}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfechfgmgbgehjgpgogpfcdfejeoegfpeme}
We define $\mname{c\_2Erelation\_2EINVOL}$ to be ${{\uniddcgcg} A\_27z : {\iota} .  {{\uniddcgcg} V0f \in {({{A\_27z}^{{A\_27z}}})} .  {({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{({{A\_27z}^{{A\_27z}}})}})}}~{({{{ap}~{({{{ap}~{({{{{\mname{c\_2Ecombin\_2Eo}}~{A\_27z}}~{A\_27z}}~{A\_27z}})}}~{V0f}})}}~{V0f}})}})}}~{({{\mname{c\_2Ecombin\_2EI}}~{A\_27z}})}})}}}$.
\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} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}{\unicdcdadad} A\_27b .  nonempty~A\_27b{\unicdbdjdcd}(\\
{\unicdcdadad} V0f \in (A\_27b^{{A\_27a}}) .  ({\unicdcdadad} V1g \in (A\_27b^{{A\_27a}}) .  ((V0f=\\
V1g){\unicdbdjded}({\unicdcdadad} V2x \in A\_27a .  ((ap~V0f~V2x)=(ap~V1g~V2x))))))\end{array}
\label{hyp:ehigngpfcdfecgpgpgmgpfcdfegeffoepfpffebfpfpfefiene}
\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} A\_27c .  \\
nonempty~A\_27c{\unicdbdjdcd}({\unicdcdadad} V0f \in (A\_27b^{{A\_27a}}) .  ({\unicdcdadad} V1g \in (A\_27a^{{A\_27c}}) .  \\
({\unicdcdadad} V2x \in A\_27c .  ((ap~(ap~(ap~(\mname{c\_2Ecombin\_2Eo}~A\_27c~A\_27b~A\_27a)~\\
V0f)~V1g)~V2x)=(ap~V0f~(ap~V1g~V2x))))))\end{array}
\label{hyp:ehigngpfcdfedgpgngcgjgogpfcdfepgpfpfefiene}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}({\unicdcdadad} V0x \in A\_27a .  ((ap~(\mname{c\_2Ecombin\_2EI}~\\
A\_27a)~V0x)=V0x))\end{array}
\label{hyp:ehigngpfcdfedgpgngcgjgogpfcdfejepfpfefiene}
\end{equation}
\begin{theorem}\label{thm:ehigngpfcdfechfgmgbgehjgpgogpfcdfejeoegfpeme}
$$\begin{array}{c}{\unicdcdadad} A\_27z .  nonempty~A\_27z{\unicdbdjdcd}({\unicdcdadad} V0f \in (A\_27z^{{A\_27z}}) .  ((p~\\
(ap~(\mname{c\_2Erelation\_2EINVOL}~A\_27z)~V0f)){\unicdbdjded}({\unicdcdadad} V1x \in A\_27z .  (\\
(ap~V0f~(ap~V0f~V1x))=V1x))))\end{array}$$
\end{theorem}
\end{document}
