\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{t65\_pscomp\_1 (TMQ921yAfNej7gk5umLd5jQNs6yi6Ki5ZkS)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_pscomp\_1 : {\iota}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_pscomp\_1 : {\iota}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\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}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_euclid~\\
(k19\_euclid~X0~X1)=X0){\unicdcdcdhd}(k18\_euclid~(k19\_euclid~X0~X1)=X1)))\end{array}
\label{hyp:ehfdcdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k5\_pscomp\_1){\unicdcdcdhd}((v1\_funct\_2~k5\_pscomp\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k5\_pscomp\_1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers))))\end{array}
\label{hyp:egehpflgfdpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_pscomp\_1){\unicdcdcdhd}((v1\_funct\_2~k4\_pscomp\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k4\_pscomp\_1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers))))\end{array}
\label{hyp:egehpflgedpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k19\_euclid~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgbdjdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers))))){\unicdbdjdcd}((X0=k5\_pscomp\_1){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k1\_seq\_1~X0~X1=k18\_euclid~X1)))\end{array}
\label{hyp:eggdpfahdhdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers))))){\unicdbdjdcd}((X0=k4\_pscomp\_1){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k1\_seq\_1~X0~X1=k17\_euclid~X1)))\end{array}
\label{hyp:egfdpfahdhdgpgngahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdfdpfahdhdgpgngahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k1\_seq\_1~\\
k5\_pscomp\_1~(k19\_euclid~X0~X1)=X1){\unicdcdcdhd}(k1\_seq\_1~k4\_pscomp\_1~(k19\_euclid~\\
X0~X1)=X0)))\end{array}$$
\end{theorem}
\end{document}
