\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t7\_ntalgo\_1 (TMQSnCyjtDsaJSDjj4UmKszC4DyoT7AShXf)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_ntalgo\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_ntalgo\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k4\_numbers}}\label{hyp:mgddbdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k4\_numbers){\unicdbdjdcd}(((X1=\\
k6\_int\_1~X0~X2){\unicdcdcdhd}(k3\_mcart\_1~k4\_numbers~k4\_numbers~k4\_numbers~\\
(k2\_ntalgo\_1~X2~X1)=np\_\_1)){\unicdbdjdcd}((X2=k6\_numbers){\unicdcdcdid}(k6\_int\_1~(k3\_xcmplx\_0~\\
(k3\_ntalgo\_1~X0~X2)~X0)~X2=k6\_int\_1~np\_\_1~X2)))))\end{array}
\label{hyp:mgcdddpfogehbgmghgpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{m1\_subset\_1}~{np\_\_1}}~{k4\_numbers}})}{\unicdcdcdhd}{({{{m1\_subset\_1}~{k6\_numbers}}~{k4\_numbers}})}}\label{hyp:mgbdfdpfdgbgchegggjgogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k3\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k4\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k4\_numbers)){\unicdbdjdcd}(m1\_subset\_1~(k3\_ntalgo\_1~X0~X1)~k4\_numbers)\end{array}
\label{hyp:egehpflgddpfogehbgmghgpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(((X1{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}\\
(k6\_int\_1~X0~X1=k6\_xcmplx\_0~X0~(k3\_xcmplx\_0~(k5\_int\_1~X0~X1)~X1))){\unicdcdcdhd}\\
((X1=k6\_numbers){\unicdbdjdcd}(k6\_int\_1~X0~X1=k6\_numbers))))\end{array}
\label{hyp:egbdadpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_numbers}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgbdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfogehbgmghgpgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k4\_numbers){\unicdbdjdcd}(((X2=\\
k6\_int\_1~X0~X1){\unicdcdcdhd}(k3\_mcart\_1~k4\_numbers~k4\_numbers~k4\_numbers~\\
(k2\_ntalgo\_1~X1~X2)=np\_\_1)){\unicdbdjdcd}(k6\_int\_1~(k3\_xcmplx\_0~(k3\_ntalgo\_1~\\
X0~X1)~X0)~X1=k6\_int\_1~np\_\_1~X1))))\end{array}$$
\end{theorem}
\end{document}
