\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{l4\_ntalgo\_1 (TMd7VMkEwwCVH8B3GkU8Pk7XZqgbBd5k7f8)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_int\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ((X0~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k2\_nat\_1~X1~np\_\_1))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(k8\_nat\_1~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~X3){\unicdbdjded}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}(k1\_funct\_1~X2~X4=k1\_funct\_1~\\
X3~X4))))\end{array}
\label{hyp:egidpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:mgedpfogehbgmghgpgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((\\
v1\_funct\_2~X3~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdbdjdcd}(((\\
k8\_nat\_1~k5\_numbers~X2~k6\_numbers=k1\_int\_2~X0){\unicdcdcdhd}((k8\_nat\_1~k5\_numbers~\\
X3~k6\_numbers=k1\_int\_2~X1){\unicdcdcdhd}(({\unicdcdadad} X6 .  (m2\_subset\_1~X6~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((k8\_nat\_1~k5\_numbers~X2~(k2\_nat\_1~X6~np\_\_1)=k8\_nat\_1~\\
k5\_numbers~X3~X6){\unicdcdcdhd}(k8\_nat\_1~k5\_numbers~X3~(k2\_nat\_1~X6~np\_\_1)=\\
k4\_nat\_d~(k8\_nat\_1~k5\_numbers~X2~X6)~(k8\_nat\_1~k5\_numbers~X3~X6)))){\unicdcdcdhd}\\
((k8\_nat\_1~k5\_numbers~X4~k6\_numbers=k1\_int\_2~X0){\unicdcdcdhd}((k8\_nat\_1~\\
k5\_numbers~X5~k6\_numbers=k1\_int\_2~X1){\unicdcdcdhd}({\unicdcdadad} X6 .  (m2\_subset\_1~\\
X6~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k8\_nat\_1~k5\_numbers~X4~(k2\_nat\_1~\\
X6~np\_\_1)=k8\_nat\_1~k5\_numbers~X5~X6){\unicdcdcdhd}(k8\_nat\_1~k5\_numbers~X5~(\\
k2\_nat\_1~X6~np\_\_1)=k4\_nat\_d~(k8\_nat\_1~k5\_numbers~X4~X6)~(k8\_nat\_1~\\
k5\_numbers~X5~X6))))))))){\unicdbdjdcd}((r2\_funct\_2~k5\_numbers~k5\_numbers~\\
X2~X4){\unicdcdcdhd}(r2\_funct\_2~k5\_numbers~k5\_numbers~X3~X5))))))))\end{array}$$
\end{theorem}
\end{document}
