\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{t15\_taylor\_1 (TMPPutBYyEL791x8C2h6mdBgxRYA7Ao3ayo)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_sin\_cos : {\iota}$ be given.
Let $ k5\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_power : {\iota}$ be given.
Let $ k25\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdbdjdcd}(k25\_sin\_cos~\\
(k5\_power~k8\_power~X0)=X0))\end{array}
\label{hyp:ehbdedpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k8\_power}}~{k1\_numbers}}\label{hyp:egehpflgidpfahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k5\_power~X0~X1))\end{array}
\label{hyp:egehpflgfdpfahpghhfgch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{{k25\_sin\_cos}~{X0}}={{{k1\_seq\_1}~{k24\_sin\_cos}}~{X0}}})}}}\label{hyp:egcdddpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfehbgjhmgpgchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdbdjdcd}(k1\_seq\_1~\\
k24\_sin\_cos~(k5\_power~k8\_power~X0)=X0))\end{array}$$
\end{theorem}
\end{document}
