\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{t63\_algspec1 (TMQcFzGxPAJWF92QjrkMkVqPbWB8SnAhZtq)}
\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 $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_msafree1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m4\_algspec1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_algspec1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ g1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_instalg1 : {{\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 $ k3\_finseq\_2 : {{\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 $ m3\_algspec1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_instalg1~X1){\unicdcdcdhd}(l1\_msualg\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}((v1\_msafree1~X2~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X2~X0))){\unicdbdjdcd}((l3\_msualg\_1~X2~X1){\unicdbdjdcd}(g1\_msualg\_1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_msualg\_1~X0)~(u2\_msualg\_1~X0)=g1\_msualg\_1~\\
(u1\_struct\_0~X1)~(u4\_struct\_0~X1)~(u1\_msualg\_1~X1)~(u2\_msualg\_1~\\
X1)))))\end{array}
\label{hyp:ehgdcdpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_instalg1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}(((r1\_tarski~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_tarski~(u1\_msualg\_1~X1)~(u1\_msualg\_1~\\
X0)){\unicdcdcdhd}(r1\_tarski~(u2\_msualg\_1~X1)~(u2\_msualg\_1~X0)))){\unicdbdjdcd}(m1\_instalg1~\\
X1~X0)))\end{array}
\label{hyp:ehbdddpfjgogdhehbgmghgbd}
\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}((r1\_tarski~(u2\_msualg\_1~X1)~(u2\_msualg\_1~\\
X0)){\unicdcdcdhd}(r1\_tarski~(u1\_msualg\_1~X1)~(u1\_msualg\_1~X0))))\end{array}
\label{hyp:ehbdbdpfjgogdhehbgmghgbd}
\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}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(r1\_tarski~(u4\_struct\_0~X1)~(u4\_struct\_0~X0))))\end{array}
\label{hyp:ehbdadpfjgogdhehbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X1~(k3\_finseq\_2~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~(k3\_finseq\_2~X0)))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (g1\_msualg\_1~X0~\\
X1~X2~X3=g1\_msualg\_1~X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}\\
(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_msualg\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u2\_msualg\_1~X0)~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(u2\_msualg\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_msualg\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_msualg\_1~X0)~(u4\_struct\_0~X0)~(k3\_finseq\_2~(\\
u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~(u1\_msualg\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u4\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpffhbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m4\_algspec1~X1~X0){\unicdbdjdcd}(m3\_algspec1~X1))\end{array}
\label{hyp:egehpfngedpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_algspec1~X1~X0){\unicdbdjdcd}((v1\_instalg1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))\end{array}
\label{hyp:egehpfngcdpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_algspec1~X1){\unicdbdjdcd}((m4\_algspec1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((\preoh v11\_struct\_0~\\
X2){\unicdcdcdhd}(m2\_algspec1~X2~X0)){\unicdcdcdhd}((v1\_msualg\_6~X1~X2){\unicdcdcdhd}(l3\_msualg\_1~X1~\\
X2)))))\end{array}
\label{hyp:eghdpfbgmghgdhahfgdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_instalg1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}((m2\_algspec1~X1~X0){\unicdbdjded}(m1\_instalg1~\\
X0~X1)))\end{array}
\label{hyp:egfdpfbgmghgdhahfgdgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdddpfbgmghgdhahfgdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_instalg1~X1){\unicdcdcdhd}(l1\_msualg\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}((v1\_msafree1~X2~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X2~X0))){\unicdbdjdcd}((m4\_algspec1~X2~X1){\unicdbdjdcd}(m2\_algspec1~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
