\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t30\_genealg1 (TMTc1LriFP96pREhS9ScU8mSCnuVPbQ6vN6)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_genealg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_genealg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k8\_genealg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k9\_genealg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}\\
((v1\_relat\_1~X4){\unicdcdcdhd}((v2\_relat\_1~X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~\\
X4))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_genealg1~X5~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_genealg1~\\
X6~X4){\unicdbdjdcd}((k10\_genealg1~X4~X5~X6~k6\_numbers~X0~X1~X2=k9\_genealg1~X4~\\
X6~X5~X0~X1~X2){\unicdcdcdhd}((k10\_genealg1~X4~X5~X6~X3~k6\_numbers~X1~X2=k9\_genealg1~\\
X4~X6~X5~X3~X1~X2){\unicdcdcdhd}((k10\_genealg1~X4~X5~X6~X3~X0~k6\_numbers~X2=k9\_genealg1~\\
X4~X6~X5~X3~X0~X2){\unicdcdcdhd}(k10\_genealg1~X4~X5~X6~X3~X0~X1~k6\_numbers=k9\_genealg1~\\
X4~X6~X5~X3~X0~X1))))))))))\end{array}
\label{hyp:ehcdjdpfhgfgogfgbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v2\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finseq\_1~X3))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_genealg1~X4~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_genealg1~X5~X3){\unicdbdjdcd}((k9\_genealg1~X3~X4~X5~k6\_numbers~X0~X1=k8\_genealg1~\\
X3~X5~X4~X0~X1){\unicdcdcdhd}((k9\_genealg1~X3~X4~X5~X2~k6\_numbers~X1=k8\_genealg1~\\
X3~X5~X4~X2~X1){\unicdcdcdhd}(k9\_genealg1~X3~X4~X5~X2~X0~k6\_numbers=k8\_genealg1~\\
X3~X5~X4~X2~X0))))))))\end{array}
\label{hyp:ehbdfdpfhgfgogfgbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
\begin{theorem}\label{thm:ehddadpfhgfgogfgbgmghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}\\
((v1\_relat\_1~X4){\unicdcdcdhd}((v2\_relat\_1~X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~\\
X4))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_genealg1~X5~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_genealg1~\\
X6~X4){\unicdbdjdcd}((k10\_genealg1~X4~X5~X6~k6\_numbers~k6\_numbers~X0~X1=k8\_genealg1~\\
X4~X5~X6~X0~X1){\unicdcdcdhd}((k10\_genealg1~X4~X5~X6~k6\_numbers~X2~k6\_numbers~X1=\\
k8\_genealg1~X4~X5~X6~X2~X1){\unicdcdcdhd}((k10\_genealg1~X4~X5~X6~k6\_numbers~X2~\\
X0~k6\_numbers=k8\_genealg1~X4~X5~X6~X2~X0){\unicdcdcdhd}((k10\_genealg1~X4~X5~X6~\\
X3~k6\_numbers~X0~k6\_numbers=k8\_genealg1~X4~X5~X6~X3~X0){\unicdcdcdhd}((k10\_genealg1~\\
X4~X5~X6~X3~k6\_numbers~k6\_numbers~X1=k8\_genealg1~X4~X5~X6~X3~X1){\unicdcdcdhd}(\\
k10\_genealg1~X4~X5~X6~X3~X2~k6\_numbers~k6\_numbers=k8\_genealg1~X4~\\
X5~X6~X3~X2))))))))))))\end{array}$$
\end{theorem}
\end{document}
