\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{t36\_algspec1 (TMM8EydyB6kNEcb3uqqUca6kasy2D5MSJpg)}
\maketitle
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_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 $ r1\_algspec1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_algspec1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_algspec1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ r3\_pua2mss1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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){\unicdbdjdcd}(((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u4\_struct\_0~X0)~(u4\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u4\_struct\_0~X1)))))))))))\end{array}
\label{hyp:ehjdpfjgogdhehbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_algspec1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k2\_algspec1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k2\_algspec1~X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k2\_algspec1~X0~X1~X2)))))\end{array}
\label{hyp:egehpflgcdpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((v1\_relat\_1~\\
(k1\_algspec1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k1\_algspec1~X0~X1)~X0){\unicdcdcdhd}((v1\_funct\_1~\\
(k1\_algspec1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k1\_algspec1~X0~X1)~X0))))\end{array}
\label{hyp:egehpflgbdpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((r1\_algspec1~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((\preoh v11\_struct\_0~X3){\unicdcdcdhd}((v1\_msualg\_1~X3){\unicdcdcdhd}(\\
l1\_msualg\_1~X3)))){\unicdbdjdcd}((X3=k2\_algspec1~X0~X1~X2){\unicdbdjded}((r3\_pua2mss1~\\
X0~X3~(k1\_algspec1~(u1\_struct\_0~X0)~X1)~(k1\_algspec1~(u4\_struct\_0~\\
X0)~X2)){\unicdcdcdhd}((u1\_struct\_0~X3=k10\_xtuple\_0~(k1\_algspec1~(u1\_struct\_0~\\
X0)~X1)){\unicdcdcdhd}(u4\_struct\_0~X3=k10\_xtuple\_0~(k1\_algspec1~(u4\_struct\_0~\\
X0)~X2)))))))))\end{array}
\label{hyp:egedpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}(((v2\_struct\_0~X0){\unicdcdcdhd}(v1\_instalg1~\\
X0)){\unicdbdjdcd}(v11\_struct\_0~X0))\end{array}
\label{hyp:dgdgedpfjgogdhehbgmghgbd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfbgmghgdhahfgdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((r1\_algspec1~X0~X1~X2){\unicdbdjdcd}((\\
v1\_funct\_1~(k1\_algspec1~(u1\_struct\_0~X0)~X1)){\unicdcdcdhd}((v1\_funct\_2~(\\
k1\_algspec1~(u1\_struct\_0~X0)~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_algspec1~X0~X1~X2))){\unicdcdcdhd}(m1\_subset\_1~(k1\_algspec1~(u1\_struct\_0~\\
X0)~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_algspec1~X0~X1~X2))))))))))\end{array}$$
\end{theorem}
\end{document}
