\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{t47\_exchsort (TMGDyxCko8CGoLbxg4GktdEjsZHpwio1wvB)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_waybel\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_exchsort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_exchsort : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_orders\_2~\\
X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}((v16\_waybel\_0~X2){\unicdcdcdhd}\\
(l1\_orders\_2~X2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~\\
X3~(u1\_struct\_0~X2)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_exchsort~X3)))){\unicdbdjdcd}(\\
(k4\_tarski~X0~X1 \in k6\_exchsort~X2~X3){\unicdbdjded}((X0 \in k9\_xtuple\_0~X3){\unicdcdcdhd}((X1 \in \\
k9\_xtuple\_0~X3){\unicdcdcdhd}((X0 \in X1){\unicdcdcdhd}(r2\_orders\_2~X2~(k7\_partfun1~(u1\_struct\_0~\\
X2)~X3~X1)~(k7\_partfun1~(u1\_struct\_0~X2)~X3~X0)))))))\end{array}
\label{hyp:ehedgdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_zfmisc\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  {\unicdcdaddd} X5 .  (X4 \in X0){\unicdcdcdhd}((X5 \in X1){\unicdcdcdhd}(X3=k4\_tarski~\\
X4~X5))))\end{array}
\label{hyp:egcdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v5\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_exchsort~\\
X1)))){\unicdbdjdcd}(k6\_exchsort~X0~X1=ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(k9\_xtuple\_0~X1)))~({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(k9\_xtuple\_0~X1)))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  (X2 \in X3){\unicdcdcdhd}(\preoh r1\_orders\_2~\\
X0~(k7\_partfun1~(u1\_struct\_0~X0)~X1~X2)~(k7\_partfun1~(u1\_struct\_0~\\
X0)~X1~X3)))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k4\_tarski~X2~X3)))\end{array}
\label{hyp:egbdbdpffgihdgigdhpgcheh}
\end{equation}
\begin{theorem}\label{thm:ehedhdpffgihdgigdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v16\_waybel\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_exchsort~X1)))){\unicdbdjdcd}(r1\_tarski~(k6\_exchsort~\\
X0~X1)~(k2\_zfmisc\_1~(k9\_xtuple\_0~X1)~(k9\_xtuple\_0~X1))))\end{array}$$
\end{theorem}
\end{document}
