\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\_sin\_cos9 (TMbTcu8zRyZd8zMjbVfnzyGKtw3hgoApYor)}
\maketitle
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k30\_sin\_cos : {\iota}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rcomp\_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 $ k1\_numbers : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k26\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k41\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k16\_sin\_cos : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k31\_sin\_cos : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(v1\_xboole\_0~\\
X1))\end{array}
\label{hyp:ehidpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(v3\_rcomp\_1~\\
(k2\_rcomp\_1~X0~X1)))\end{array}
\label{hyp:ehhdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_rcomp\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((r1\_tarski~X0~(k1\_relset\_1~k1\_numbers~k30\_sin\_cos)){\unicdbdjdcd}((r2\_fdiff\_1~\\
k30\_sin\_cos~X0){\unicdcdcdhd}(r2\_relset\_1~k1\_numbers~k1\_numbers~(k2\_fdiff\_1~\\
k30\_sin\_cos~X0)~(k5\_relset\_1~k1\_numbers~k1\_numbers~(k26\_valued\_1~\\
k1\_numbers~k1\_numbers~(k41\_valued\_1~k1\_numbers~k1\_numbers~(k6\_rfunct\_1~\\
k1\_numbers~k1\_numbers~k16\_sin\_cos))~(k1\_real\_1~np\_\_1))~X0))))\end{array}
\label{hyp:ehfdjdpfigggegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}r1\_tarski~(k2\_rcomp\_1~k6\_numbers~k32\_sin\_cos)~(k1\_relset\_1~k1\_numbers~\\
k30\_sin\_cos)\end{array}
\label{hyp:ehcdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k32\_sin\_cos}={k31\_sin\_cos}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddcdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}(v1\_xreal\_0~X0)))\end{array}
\label{hyp:chdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xreal\_0}~{k31\_sin\_cos}}\label{hyp:egehpflgddbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgcdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgedpfdhjgogpfdgpgdhjd}
${{{r2\_fdiff\_1}~{k30\_sin\_cos}}~{({{{k2\_rcomp\_1}~{k6\_numbers}}~{k32\_sin\_cos}})}}$.
\end{theorem}
\end{document}
