\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{t29\_sin\_cos7 (TMVQzM1ufBrupcNuunfDhNdUP6bSx1HNY8d)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k25\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_prepower : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k26\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_power : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_power : {\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 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k9\_prepower~(k26\_sin\_cos~np\_\_1)~\\
X0=k25\_sin\_cos~X0){\unicdcdcdhd}((k3\_power~(k26\_sin\_cos~np\_\_1)~X0=k25\_sin\_cos~\\
X0){\unicdcdcdhd}((k3\_power~k8\_power~X0=k25\_sin\_cos~X0){\unicdcdcdhd}(k9\_prepower~k8\_power~\\
X0=k25\_sin\_cos~X0))))\end{array}
\label{hyp:ehjdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_power}~{X0}}~{k6\_numbers}}={np\_\_1}})}}}\label{hyp:ehcdedpfahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{{k5\_power}~{k8\_power}}~{({{k25\_sin\_cos}~{X0}})}}={X0}})}}}\label{hyp:ehbdcdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_power}={k7\_power}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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\_xreal\_0}~{k7\_power}}\label{hyp:egehpflghdpfahpghhfgch}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfdhjgogpfdgpgdhhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(k25\_sin\_cos~\\
X0=np\_\_1))\end{array}$$
\end{theorem}
\end{document}
