\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{l60\_sin\_cos2 (TMMUzYyCFs8Weoe8TCYhXJyGMbzQtde3UhE)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_sin\_cos2 : {\iota}$ be given.
Let $ k4\_sin\_cos2 : {\iota}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((r1\_fdiff\_1~k4\_sin\_cos2~X0){\unicdcdcdhd}(k1\_fdiff\_1~\\
k4\_sin\_cos2~X0=k1\_seq\_1~k1\_sin\_cos2~X0))\end{array}
\label{hyp:ehddcdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((r1\_fdiff\_1~k1\_sin\_cos2~X0){\unicdcdcdhd}(k1\_fdiff\_1~\\
k1\_sin\_cos2~X0=k1\_seq\_1~k4\_sin\_cos2~X0))\end{array}
\label{hyp:ehddbdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k1\_seq\_1~k4\_sin\_cos2~X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~(k1\_seq\_1~k4\_sin\_cos2~X0)~k6\_numbers){\unicdcdcdhd}(k1\_seq\_1~\\
k4\_sin\_cos2~k6\_numbers=np\_\_1)))\end{array}
\label{hyp:ehbdfdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k9\_real\_1~(k5\_square\_1~(k1\_seq\_1~\\
k4\_sin\_cos2~X0))~(k5\_square\_1~(k1\_seq\_1~k1\_sin\_cos2~X0))=np\_\_1){\unicdcdcdhd}\\
(k9\_real\_1~(k8\_real\_1~(k1\_seq\_1~k4\_sin\_cos2~X0)~(k1\_seq\_1~k4\_sin\_cos2~\\
X0))~(k8\_real\_1~(k1\_seq\_1~k1\_sin\_cos2~X0)~(k1\_seq\_1~k1\_sin\_cos2~\\
X0))=np\_\_1))\end{array}
\label{hyp:ehbdedpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_fdiff\_1~X2~X0){\unicdcdcdhd}(r1\_fdiff\_1~\\
X1~X0)){\unicdbdjdcd}((k1\_seq\_1~X1~X0=k6\_numbers){\unicdcdcdid}((r1\_fdiff\_1~(k3\_rfunct\_1~\\
k1\_numbers~k1\_numbers~X2~X1)~X0){\unicdcdcdhd}(k1\_fdiff\_1~(k3\_rfunct\_1~k1\_numbers~\\
k1\_numbers~X2~X1)~X0=k10\_real\_1~(k9\_real\_1~(k8\_real\_1~(k1\_fdiff\_1~\\
X2~X0)~(k1\_seq\_1~X1~X0))~(k8\_real\_1~(k1\_fdiff\_1~X1~X0)~(k1\_seq\_1~\\
X2~X0)))~(k5\_square\_1~(k1\_seq\_1~X1~X0))))))))\end{array}
\label{hyp:ehbdedpfggegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_sin\_cos2){\unicdcdcdhd}((v1\_funct\_2~k4\_sin\_cos2~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k4\_sin\_cos2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgedpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_sin\_cos2){\unicdcdcdhd}((v1\_funct\_2~k1\_sin\_cos2~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k1\_sin\_cos2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgbdpfdhjgogpfdgpgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mggdadpfdhjgogpfdgpgdhcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((r1\_fdiff\_1~(k3\_rfunct\_1~k1\_numbers~\\
k1\_numbers~k1\_sin\_cos2~k4\_sin\_cos2)~X0){\unicdcdcdhd}(k1\_fdiff\_1~(k3\_rfunct\_1~\\
k1\_numbers~k1\_numbers~k1\_sin\_cos2~k4\_sin\_cos2)~X0=k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k1\_seq\_1~k4\_sin\_cos2~X0))))\end{array}$$
\end{theorem}
\end{document}
