\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{t10\_instalg1 (TMS8ehAkGkfpTE79M6nRhDHJ4zXjys51W2L)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_instalg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_pua2mss1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k10\_xtuple\_0}~{({{k4\_relat\_1}~{X0}})}}={X0}}}\label{hyp:chegcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k4\_relat\_1~\\
X0)~X0){\unicdcdcdhd}((v1\_funct\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}(v1\_partfun1~(k4\_relat\_1~\\
X0)~X0)))\end{array}
\label{hyp:ggdgbdbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_instalg1~X1~X0){\unicdbdjdcd}(l1\_msualg\_1~X1))\end{array}
\label{hyp:egehpfngbdpfjgogdhehbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l1\_msualg\_1~X1){\unicdbdjdcd}((m1\_instalg1~X1~X0){\unicdbdjded}(r3\_pua2mss1~X1~X0~(k6\_partfun1~\\
(u1\_struct\_0~X1))~(k6\_partfun1~(u4\_struct\_0~X1)))))\end{array}
\label{hyp:egcdpfjgogdhehbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_msualg\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}((r3\_pua2mss1~X0~X1~X2~X3){\unicdbdjded}((k9\_xtuple\_0~\\
X2=u1\_struct\_0~X0){\unicdcdcdhd}((k9\_xtuple\_0~X3=u4\_struct\_0~X0){\unicdcdcdhd}((r1\_tarski~\\
(k10\_xtuple\_0~X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~\\
X3)~(u4\_struct\_0~X1)){\unicdcdcdhd}((k3\_relat\_1~(u2\_msualg\_1~X0)~X2=k3\_relat\_1~\\
X3~(u2\_msualg\_1~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}\\
(v1\_funct\_1~X5)){\unicdbdjdcd}(((X4 \in u4\_struct\_0~X0){\unicdcdcdhd}(X5=k1\_funct\_1~(u1\_msualg\_1~\\
X0)~X4)){\unicdbdjdcd}(k3\_relat\_1~X5~X2=k1\_funct\_1~(u1\_msualg\_1~X1)~(k1\_funct\_1~\\
X3~X4)))))))))))))\end{array}
\label{hyp:egbdcdpfahfhbgcdngdhdhbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfjgogdhehbgmghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_instalg1~X1~X0){\unicdbdjdcd}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(r1\_tarski~(u4\_struct\_0~X1)~(u4\_struct\_0~X0))))\end{array}$$
\end{theorem}
\end{document}
