\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{l27\_integr16 (TMJ4ynRoyG18ZHCzAvo61XXeMsy2Mr7UrxC)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k1\_numbers : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_comseq\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_comseq\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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~k2\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}(r2\_relset\_1~k1\_numbers~k1\_numbers~(k6\_comseq\_3~\\
k1\_numbers~(k2\_partfun1~k1\_numbers~k2\_numbers~X0~X1))~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~(k6\_comseq\_3~k1\_numbers~X0)~X1)))\end{array}
\label{hyp:ehddpfjgogehfghgchbdgd}
\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~k2\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}(r2\_relset\_1~k1\_numbers~k1\_numbers~(k5\_comseq\_3~\\
k1\_numbers~(k2\_partfun1~k1\_numbers~k2\_numbers~X0~X1))~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~(k5\_comseq\_3~k1\_numbers~X0)~X1)))\end{array}
\label{hyp:ehcdpfjgogehfghgchbdgd}
\end{equation}
\begin{theorem}\label{thm:mgcdhdpfjgogehfghgchbdgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k2\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}((r2\_relset\_1~k1\_numbers~k1\_numbers~(k5\_comseq\_3~\\
k1\_numbers~(k2\_partfun1~k1\_numbers~k2\_numbers~X0~X1))~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~(k5\_comseq\_3~k1\_numbers~X0)~X1)){\unicdcdcdhd}(r2\_relset\_1~\\
k1\_numbers~k1\_numbers~(k6\_comseq\_3~k1\_numbers~(k2\_partfun1~k1\_numbers~\\
k2\_numbers~X0~X1))~(k2\_partfun1~k1\_numbers~k1\_numbers~(k6\_comseq\_3~\\
k1\_numbers~X0)~X1))))\end{array}$$
\end{theorem}
\end{document}
