\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{t38\_instalg1 (TMbn6QjMWPDVUs4srF8oc9HNNmUQ9BC4okR)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_pua2mss1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_instalg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ r1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_msualg\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
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 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}(\\
l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((r3\_pua2mss1~X1~X0~X3~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
(v4\_msualg\_1~X5~X1){\unicdcdcdhd}(l3\_msualg\_1~X5~X1)){\unicdbdjdcd}((X5=k1\_instalg1~X1~\\
X0~X2~X3~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_rewrite1~(k3\_msualg\_6~\\
X1)~X6~X7){\unicdbdjdcd}((r1\_rewrite1~(k3\_msualg\_6~X0)~(k3\_funct\_2~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)~X3~X6)~(k3\_funct\_2~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)~X3~X7)){\unicdcdcdhd}({\unicdcdadad} X8 .  (m2\_msualg\_6~X8~X1~X5~X6~X7){\unicdbdjdcd}(m2\_msualg\_6~\\
X8~X0~X2~(k3\_funct\_2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X3~X6)~(k3\_funct\_2~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X3~X7))))))))))))))\end{array}
\label{hyp:mgedbdpfjgogdhehbgmghgbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfjgogdhehbgmghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}(\\
l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((r3\_pua2mss1~X1~X0~X3~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
(v4\_msualg\_1~X5~X1){\unicdcdcdhd}(l3\_msualg\_1~X5~X1)){\unicdbdjdcd}((X5=k1\_instalg1~X1~\\
X0~X2~X3~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_rewrite1~(k3\_msualg\_6~\\
X1)~X6~X7){\unicdbdjdcd}({\unicdcdadad} X8 .  (m2\_msualg\_6~X8~X1~X5~X6~X7){\unicdbdjdcd}(m2\_msualg\_6~\\
X8~X0~X2~(k3\_funct\_2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X3~X6)~(k3\_funct\_2~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X3~X7)))))))))))))\end{array}$$
\end{theorem}
\end{document}
