\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{l103\_sincos10 (TMcyDF6URE1PxGeDwcJt6FuJVrJjgz6ZdDi)}
\maketitle
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_fdiff\_9 : {\iota}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\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 $ v5\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((v5\_valued\_0~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X1~X0)){\unicdcdcdid}(v6\_valued\_0~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~X1~X0))){\unicdbdjdcd}(v2\_funct\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
X1~X0)))\end{array}
\label{hyp:ehidpfggdgpgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
X0~X1){\unicdcdcdhd}(v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~X1))){\unicdbdjdcd}\\
(v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~X0)))\end{array}
\label{hyp:ehcdjdpfchggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~k2\_fdiff\_9~(k3\_rcomp\_1~\\
(k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))~k6\_numbers))\end{array}
\label{hyp:ehbdjdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}r1\_tarski~(k1\_rcomp\_1~(k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))~\\
(k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_4)))~(k3\_rcomp\_1~(k1\_real\_1~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_2))~k6\_numbers)\end{array}
\label{hyp:mgddbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_fdiff\_9){\unicdcdcdhd}(m1\_subset\_1~k2\_fdiff\_9~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgcdpfggegjgggggpfjd}
\end{equation}
\begin{theorem}\label{thm:mgbdadddpfdhjgogdgpgdhbdad}
$$\begin{array}{c}v2\_funct\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~k2\_fdiff\_9~(k1\_rcomp\_1~\\
(k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))~(k1\_real\_1~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_4))))\end{array}$$
\end{theorem}
\end{document}
