\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{t31\_c0sp2 (TMRAbPBGXjH7m7At6i7NYm2soMiSKtxrac7)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_c0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_c0sp2 : {{\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 $ 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.
Let $ v1\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(k6\_c0sp2~X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  (v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(u1\_struct\_0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~k1\_numbers))))))~\\
({\uniddcgcg} X1 : \iota .  (v1\_pscomp\_1~X1~X0){\unicdcdcdhd}({\unicdcdaddd} X2 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}((v2\_compts\_1~\\
X2~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((X3=k13\_pre\_poly~X1){\unicdbdjdcd}(m1\_subset\_1~(k2\_pre\_topc~X0~X3)~\\
(k1\_zfmisc\_1~X2)))))))~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:eggdpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(k2\_c0sp2~X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  (v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(u1\_struct\_0~X0)~k1\_numbers){\unicdcdcdhd}((v1\_pscomp\_1~X1~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
k1\_numbers)))))))~({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egcdpfdgaddhahcd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1 \in k6\_c0sp2~X0){\unicdbdjdcd}(X1 \in k2\_c0sp2~X0))\end{array}$$
\end{theorem}
\end{document}
