\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{t32\_integra8 (TMFSXorcoBgs42ip9rhkwhcsSU68ugnHqHs)}
\maketitle
Let $ k2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_sin\_cos : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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.
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((r2\_fdiff\_1~k24\_sin\_cos~k1\_numbers){\unicdcdcdhd}\\
((r2\_fdiff\_1~k24\_sin\_cos~(k2\_subset\_1~k1\_numbers)){\unicdcdcdhd}(({\unicdcdadad} X0 .  \\
(m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k1\_fdiff\_1~k24\_sin\_cos~X0=k1\_seq\_1~\\
k24\_sin\_cos~X0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(\\
\preoh r1\_xxreal\_0~(k1\_fdiff\_1~k24\_sin\_cos~X0)~k6\_numbers)){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k2\_subset\_1~k1\_numbers){\unicdcdcdhd}((k1\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k2\_subset\_1~k1\_numbers){\unicdcdcdhd}(k2\_relset\_1~\\
k1\_numbers~k24\_sin\_cos=k3\_limfunc1~k6\_numbers)))))))\end{array}
\label{hyp:ehbdgdpfehbgjhmgpgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k24\_sin\_cos){\unicdcdcdhd}((v1\_funct\_2~k24\_sin\_cos~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k24\_sin\_cos~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdedpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r2\_fdiff\_1~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}((X2=k2\_fdiff\_1~X0~X1){\unicdbdjded}((k1\_relset\_1~k1\_numbers~\\
X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(k1\_seq\_1~\\
X2~X3=k1\_fdiff\_1~X0~X3)))))))\end{array}
\label{hyp:eghdpfggegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_subset\_1}~{X0}}={X0}}}\label{hyp:egddpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfjgogehfghgchbgid}
${{{{k2\_fdiff\_1}~{k24\_sin\_cos}}~{k1\_numbers}}={k24\_sin\_cos}}$.
\end{theorem}
\end{document}
