\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}
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\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{l104\_toprealb (TMWvhniezbzoQVMPBD6Pxbpnr1nzQcDQoHa)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_toprealb : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_sin\_cos6 : {\iota}$ 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 $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_topalg\_2 : {\iota}$ be given.
Let $ k5\_toprealb : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{{{k1\_relset\_1}~{k1\_numbers}}~{k4\_sin\_cos6}}={{{k1\_rcomp\_1}~{({{k1\_real\_1}~{np\_\_1}})}}~{np\_\_1}}}\label{hyp:ehidgdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_relset\_1}~{k1\_numbers}}~{k4\_sin\_cos6}}={{{k1\_rcomp\_1}~{k6\_numbers}}~{k32\_sin\_cos}}}\label{hyp:ehidfdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_funct\_1}~{k4\_sin\_cos6}})}{\unicdcdcdhd}{({{v1\_fcont\_1}~{k4\_sin\_cos6}})}}\label{hyp:ggdghdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_fcont\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k6\_toprealb~X0)){\unicdcdcdhd}((v1\_funct\_2~(k6\_toprealb~X0)~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_relset\_1~k1\_numbers~\\
X0))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~\\
k1\_numbers~X0))))){\unicdcdcdhd}(v5\_pre\_topc~(k6\_toprealb~X0)~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_relset\_1~k1\_numbers~X0)))~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~k1\_numbers~X0))))))\end{array}
\label{hyp:ggdgbdhdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((v1\_funct\_1~(k6\_toprealb~X0)){\unicdcdcdhd}(\\
(v1\_funct\_2~(k6\_toprealb~X0)~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_relset\_1~k1\_numbers~X0))))~(u1\_struct\_0~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~k1\_numbers~X0))))){\unicdcdcdhd}(m1\_subset\_1~\\
(k6\_toprealb~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_relset\_1~k1\_numbers~X0))))~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~k1\_numbers~\\
X0)))))))))\end{array}
\label{hyp:egehpflggdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_sin\_cos6){\unicdcdcdhd}(m1\_subset\_1~k4\_sin\_cos6~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgedpfdhjgogpfdgpgdhgd}
\end{equation}
\begin{theorem}\label{thm:mgbdadedpfehpgahchfgbgmgcg}
$$\begin{array}{c}(v1\_funct\_1~(k6\_toprealb~k4\_sin\_cos6)){\unicdcdcdhd}((v1\_funct\_2~(k6\_toprealb~\\
k4\_sin\_cos6)~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos))))){\unicdcdcdhd}\\
((v5\_pre\_topc~(k6\_toprealb~k4\_sin\_cos6)~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1)))~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos)))){\unicdcdcdhd}\\
(m1\_subset\_1~(k6\_toprealb~k4\_sin\_cos6)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~\\
(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos)))))))))\end{array}$$
\end{theorem}
\end{document}
