\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{t43\_exchsort (TMQHJ323V9FJxgLXMyb5rDfCdG3SfHXzyaB)}
\maketitle
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 $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_exchsort : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_exchsort~\\
X1))){\unicdbdjdcd}((m1\_exchsort~X0~X1){\unicdbdjdcd}(m1\_exchsort~X1~X0)))\end{array}
\label{hyp:ehddjdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
\preoh (X1 \in k9\_xtuple\_0~X0){\unicdcdcdhd}((X2 \in k9\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X0)){\unicdcdcdhd}((v3\_funct\_2~\\
X3~(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X0))))))){\unicdbdjdcd}(k2\_funct\_7~\\
(k2\_funct\_7~X0~X1~(k1\_funct\_1~X0~X2))~X2~(k1\_funct\_1~X0~X1){\unicdcdgdad}k3\_relat\_1~\\
X3~X0))))\end{array}
\label{hyp:ehbdbdbdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~\\
X0)){\unicdbdjdcd}((v1\_relat\_1~(k10\_funct\_7~X0~X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(k10\_funct\_7~\\
X0~X1~X2)))\end{array}
\label{hyp:ggdgbdcdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_exchsort~X0))){\unicdbdjdcd}(v1\_exchsort~(k10\_funct\_7~X0~X1~X2))\end{array}
\label{hyp:ggdgbdadpffgihdgigdhpgcheh}
\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}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_exchsort~\\
X1))){\unicdbdjdcd}((m1\_exchsort~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X0)){\unicdcdcdhd}((v3\_funct\_2~X2~(k9\_xtuple\_0~\\
X0)~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X0))))))){\unicdcdcdhd}(X1=k3\_relat\_1~X2~X0))))\end{array}
\label{hyp:egjdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
(((X1 \in k9\_xtuple\_0~X0){\unicdcdcdhd}(X2 \in k9\_xtuple\_0~X0)){\unicdbdjdcd}(k10\_funct\_7~X0~\\
X1~X2=k2\_funct\_7~(k2\_funct\_7~X0~X1~(k1\_funct\_1~X0~X2))~X2~(k1\_funct\_1~\\
X0~X1))){\unicdcdcdhd}((\preoh (X1 \in k9\_xtuple\_0~X0){\unicdcdcdhd}(X2 \in k9\_xtuple\_0~X0)){\unicdbdjdcd}(k10\_funct\_7~\\
X0~X1~X2=X0)))\end{array}
\label{hyp:egbdcdpfggfhogdgehpfhd}
\end{equation}
\begin{theorem}\label{thm:ehedddpffgihdgigdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_exchsort~X2))){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~X2){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~\\
X2)){\unicdbdjdcd}((m1\_exchsort~(k10\_funct\_7~X2~X0~X1)~X2){\unicdcdcdhd}(m1\_exchsort~X2~\\
(k10\_funct\_7~X2~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
