\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{t54\_exchsort (TMUvyfsgqbys2yEhNuer3ah9Wrhk4gSuPFs)}
\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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_exchsort : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\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 $ v1\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
k9\_xtuple\_0~(k10\_funct\_7~X0~X1~X2)=k9\_xtuple\_0~X0)\end{array}
\label{hyp:ehjdjdpfggfhogdgehpfhd}
\end{equation}
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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v5\_relat\_1~X4~X0){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_exchsort~X4)))){\unicdbdjdcd}\\
((X1 \in k9\_xtuple\_0~X4){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((X1=X3){\unicdcdcdid}(k7\_partfun1~X0~(k10\_funct\_7~\\
X4~X2~X3)~X1=k7\_partfun1~X0~X4~X1))))\end{array}
\label{hyp:ehddedpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v5\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_exchsort~X3)))){\unicdbdjdcd}((\\
(X1 \in k9\_xtuple\_0~X3){\unicdcdcdhd}(X2 \in k9\_xtuple\_0~X3)){\unicdbdjdcd}(k7\_partfun1~X0~(k10\_funct\_7~\\
X3~X1~X2)~X2=k7\_partfun1~X0~X3~X1))\end{array}
\label{hyp:ehddcdpffgihdgigdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_ordinal1~X2){\unicdbdjdcd}(((X0 \in X1){\unicdcdcdhd}\\
(X1 \in X2)){\unicdbdjdcd}(X0 \in X2))\end{array}
\label{hyp:ehbdadpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X1){\unicdcdcdhd}\\
((v5\_relat\_1~X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}(v5\_relat\_1~(k10\_funct\_7~\\
X1~X2~X3)~X0)\end{array}
\label{hyp:ggdgidpffgihdgigdhpgcheh}
\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}\\
(v1\_ordinal6~(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgbdpffgihdgigdhpgcheh}
\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\_ordinal6~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v3\_ordinal1~X1))\end{array}
\label{hyp:dgdgcdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{v1\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v2\_ordinal1}~{X0}})}})}}}\label{hyp:dgdgbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({\preoh{{{X1} \in {X0}}}})}}}}\label{hyp:bgogehjgdhjhngngfgehchjhpfchcdpfigjgegegfgog}
\end{equation}
\begin{theorem}\label{thm:ehfdedpffgihdgigdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}\\
((v3\_orders\_2~X3){\unicdcdcdhd}((v4\_orders\_2~X3){\unicdcdcdhd}((v5\_orders\_2~X3){\unicdcdcdhd}((v16\_waybel\_0~\\
X3){\unicdcdcdhd}(l1\_orders\_2~X3)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~\\
X4~(u1\_struct\_0~X3)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_exchsort~X4)))){\unicdbdjdcd}(\\
(k4\_tarski~X0~X1 \in k6\_exchsort~X3~X4){\unicdbdjdcd}((k4\_tarski~X2~X0 \in k6\_exchsort~\\
X3~X4){\unicdbdjded}((X2 \in X0){\unicdcdcdhd}(k4\_tarski~X2~X1 \in k6\_exchsort~X3~(k10\_funct\_7~\\
X4~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
