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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t80\_exchsort (TMLaX8eVZLHZrojUhmQVKxzzB5pa9dihhaj)}
\maketitle
Let $ k4\_exchsort : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_exchsort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k3\_tarski}~{({{k1\_ordinal1}~{X0}})}}={X0}})}}}\label{hyp:ehcdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_ordinal1}~{np\_\_0}}={np\_\_1}}\label{hyp:chbhdffhdgdgpfpflgbdpfpgchegjgogbgmgbdpfpfchadpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_afinsq\_1}~{X0}}={{k3\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v5\_ordinal1~(k3\_afinsq\_1~X0)){\unicdcdcdhd}(v1\_finset\_1~(k3\_afinsq\_1~\\
X0))\end{array}
\label{hyp:ggdgidpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k3\_afinsq\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k3\_afinsq\_1~\\
X0))\end{array}
\label{hyp:ggdghdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}\\
(k4\_exchsort~X0=k1\_funct\_1~X0~(k3\_tarski~(k9\_xtuple\_0~X0)))\end{array}
\label{hyp:eghdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=\\
k5\_afinsq\_1~X0){\unicdbdjded}((k9\_xtuple\_0~X1=np\_\_1){\unicdcdcdhd}(k1\_funct\_1~X1~k6\_numbers=\\
X0)))\end{array}
\label{hyp:egedpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgddpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0)))\end{array}
\label{hyp:dgdgbdpffgihdgigdhpgcheh}
\end{equation}
\begin{theorem}\label{thm:ehidadpffgihdgigdhpgcheh}
${{\unicdcdadad} X0 .  {{{k4\_exchsort}~{({{k5\_afinsq\_1}~{X0}})}}={X0}}}$.
\end{theorem}
\end{document}
