\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{t36\_sublemma (TMGgVXY3Xo2UL3TTtEmqCao7NLrpVT3RPqW)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k24\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k23\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_sublemma~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_substut1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_substut1~X4~X0~X3){\unicdbdjdcd}(((v3\_substut1~X1~X0){\unicdcdcdhd}((v3\_substut1~X3~\\
X0){\unicdcdcdhd}(k24\_substut1~X0~X1~X2=k24\_substut1~X0~X3~X4))){\unicdbdjdcd}((k23\_substut1~\\
X0~X1=k23\_substut1~X0~X3){\unicdcdcdhd}(X2=X4)))))))\end{array}
\label{hyp:ehddfdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_sublemma~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_substut1~X2~X0~X1){\unicdbdjdcd}((v3\_substut1~X1~X0){\unicdbdjdcd}(k9\_sublemma~\\
X0~X1~X2=k24\_substut1~X0~X1~X2))))\end{array}
\label{hyp:egfdpfdhfhcgmgfgngngbg}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_sublemma~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_substut1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_substut1~X4~X0~X3){\unicdbdjdcd}(((v3\_substut1~X1~X0){\unicdcdcdhd}((v3\_substut1~X3~\\
X0){\unicdcdcdhd}(k9\_sublemma~X0~X1~X2=k24\_substut1~X0~X3~X4))){\unicdbdjdcd}((k23\_substut1~\\
X0~X1=k23\_substut1~X0~X3){\unicdcdcdhd}(X2=X4)))))))\end{array}$$
\end{theorem}
\end{document}
