\documentclass{article}
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\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}
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\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{t40\_sublemma (TMMEth3Ux9cfAnrGHdYo9cpjS4eWL7Av3K1)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k38\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k35\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_sublemma : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_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 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_substut1~X3~X0~(k7\_sublemma~\\
X0~X2~X1)){\unicdbdjdcd}(\preoh (v3\_substut1~(k7\_sublemma~X0~X2~X1)~X0){\unicdcdcdhd}((\preoh X1 \in k10\_xtuple\_0~\\
(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~X1~(k2\_sublemma~X0~X2))~X3)){\unicdcdcdhd}\\
(k35\_substut1~X0~(k32\_substut1~X0~(k9\_sublemma~X0~(k7\_sublemma~\\
X0~X2~X1)~X3)) \in k10\_xtuple\_0~(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~\\
X1~(k2\_sublemma~X0~X2))~X3)))))))\end{array}
\label{hyp:ehddjdpfdhfhcgmgfgngngbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_substut1~X3~X0~(k7\_sublemma~\\
X0~X2~X1)){\unicdbdjdcd}(((v3\_substut1~(k7\_sublemma~X0~X2~X1)~X0){\unicdcdcdhd}(X1 \in k10\_xtuple\_0~\\
(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~X1~(k2\_sublemma~X0~X2))~X3))){\unicdbdjdcd}\\
((\preoh k35\_substut1~X0~(k32\_substut1~X0~(k9\_sublemma~X0~(k7\_sublemma~\\
X0~X2~X1)~X3)) \in k10\_xtuple\_0~(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~\\
X1~(k2\_sublemma~X0~X2))~X3)){\unicdcdcdhd}(\preoh k35\_substut1~X0~(k32\_substut1~X0~\\
(k9\_sublemma~X0~(k7\_sublemma~X0~X2~X1)~X3)) \in k9\_substut1~X0~(k2\_sublemma~\\
X0~X2)))))))\end{array}
\label{hyp:ehddidpfdhfhcgmgfgngngbg}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdhfhcgmgfgngngbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k16\_substut1~\\
X0)~(k38\_substut1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_substut1~X3~X0~(k7\_sublemma~\\
X0~X2~X1)){\unicdbdjdcd}(\preoh (v3\_substut1~(k7\_sublemma~X0~X2~X1)~X0){\unicdcdcdhd}(k35\_substut1~\\
X0~(k32\_substut1~X0~(k9\_sublemma~X0~(k7\_sublemma~X0~X2~X1)~X3)) \in \\
k10\_xtuple\_0~(k7\_substut1~X0~X1~(k11\_cqc\_lang~X0~X1~(k2\_sublemma~\\
X0~X2))~X3))))))\end{array}$$
\end{theorem}
\end{document}
